I built an example with a mindmap as figure and three blocks as explanation text (just to use both block, alertblock and exampleblock).
The code used to create the mindmap is taken from How to shade mindmap concepts?, so maybe you are not interested in, but I think this could be useful to show you also how to present figures dynamically, not only blocks.
Here is the code (commented such that you can skip the part useful for the mindmap):
\documentclass{beamer}
\usepackage{lmodern}
%%% Theme definitions
\usetheme{Singapore}
\usecolortheme{rose} % to have colored blocks
\setbeamertemplate{blocks}[rounded][shadow=true]
\usepackage{tikz}
\usetikzlibrary{mindmap}
% ---- from now starts code useful to draw the mindmap
%%% Overlay definitions
% based on Daniel's code
% https://tex.stackexchange.com/questions/55806/tikzpicture-in-beamer/55849#55849
\tikzset{
invisible/.style={opacity=0},
visible on/.style={alt=#1{}{invisible}},
alt/.code args={<#1>#2#3}{%
\alt<#1>{\pgfkeysalso{#2}}{\pgfkeysalso{#3}}
}
}
%%% Shadings definitions
% based on
% https://tex.stackexchange.com/questions/58249/how-to-add-shade-to-mindmap-concept/62097#62097
\makeatletter
\pgfdeclareradialshading[tikz@ball]{myball}{\pgfqpoint{5bp}{10bp}}{%
color(0bp)=(tikz@ball!30!white);
color(9bp)=(tikz@ball!75!white);
color(18bp)=(tikz@ball!90!black);
color(25bp)=(tikz@ball!70!black);
color(50bp)=(black)}
% to make possible use "myball color=..."
\tikzoption{myball color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{myball}\tikz@addmode{\tikz@mode@shadetrue}}
\pgfdeclareradialshading[tikz@ball]{myball-left}{\pgfqpoint{5bp}{-9bp}}{%
color(0bp)=(tikz@ball!30!white);
color(15bp)=(tikz@ball!75!white);
color(25bp)=(tikz@ball!90!black);
color(40bp)=(tikz@ball!70!black);
color(70bp)=(black)}
\tikzoption{myball-left color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{myball-left}\tikz@addmode{\tikz@mode@shadetrue}}
\pgfdeclareradialshading[tikz@ball]{myball-right}{\pgfqpoint{-5bp}{-9bp}}{%
color(0bp)=(tikz@ball!30!white);
color(15bp)=(tikz@ball!75!white);
color(25bp)=(tikz@ball!90!black);
color(40bp)=(tikz@ball!70!black);
color(70bp)=(black)}
\tikzoption{myball-right color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{myball-right}\tikz@addmode{\tikz@mode@shadetrue}}
\makeatother
\tikzset{level 1 concept/.append style={font=\sf, sibling angle=90,level distance = 25mm}}
\tikzset{level 2 concept/.append style={font=\sf, sibling angle=45,level distance = 16mm}}
\tikzset{level 3 concept/.append style={font=\sf, sibling angle=45,level distance = 17mm}}
\tikzset{every node/.append style={scale=0.45}}
% ---- end of code useful to draw the mindmap
\begin{document}
\begin{frame}{Title}
\begin{columns}
% Figure
\begin{column}{0.49\textwidth}
\begin{tikzpicture}[mindmap, concept color=blue, font=\sf\bf, text=white,scale=0.7]
\node[circle,shading=myball,visible on=<1->]{Root Concept}[clockwise from=315]
child [concept color=orange,visible on=<2->] {node[circle, myball-left color=orange] (c1){Child 1}
child[visible on=<3->] {node [circle, myball-left color=orange](c11){Child 1-1}}
child[visible on=<3->] {node [circle,myball-left color=orange](c12){Child 1-2}}
child[visible on=<3->] {node [circle,myball-left color=orange](c13){Child 1-3}}
}
child [concept color=violet,visible on=<4->]{node [circle,myball-right color=violet](c2){Child 2}
child[visible on=<5->] {node [circle,myball-right color=violet](c21){Child 2-1}}
child[visible on=<5->] {node [circle,myball-right color=violet](c22){Child 2-2}}
child[visible on=<5->] {node [circle,myball-right color=violet](c22){Child 1-3}}
};
\end{tikzpicture}
\end{column}
% Explanation Blocks
\begin{column}{0.49\textwidth}
\begin{block}<1>{Root concept explanation}
This ... consist of... because....\\
and is peculiar of...
\end{block}
\begin{exampleblock}<2,3>{Child concept}
This ... consist of... because....\\
and is peculiar of...
\end{exampleblock}
\begin{alertblock}<4,5>{Another child concept}
This ... consist of... because....\\
and is peculiar of...
\end{alertblock}
\end{column}
\end{columns}
\end{frame}
\end{document}
The result is:

To be coherent with the image, blocks related to a given concept are displayed when the concept is shown; in the picture, to decide when a new concept should be presented, it is used visible on=<value>. The same value, therefore, is applied to the block: \begin{block}<value>.... If the value does not comprise a -, that block will presented just in the moments given in value. This idea is taken from Mindmap tikzpicture in beamer (reveal step by step).
Let's change a bit the previous example to show this fact (the change is just for the block part, the rest of the code is still the same):
% Blocks
\begin{column}{0.49\textwidth}
\begin{block}<1->{Root concept explanation}
This ... consist of... because....\\
and is peculiar of...
\end{block}
\begin{exampleblock}<2,3->{Child concept}
This ... consist of... because....\\
and is peculiar of...
\end{exampleblock}
\begin{alertblock}<4,5->{Another child concept}
This ... consist of... because....\\
and is peculiar of...
\end{alertblock}
\end{column}
The result now is:

The important thing to notice is the - in all overlay specifications.
Since in the comments has been mentioned the dynblocks package, I provide a solution that makes use of it. Note: to compile the version 0.2a is required.
Code:
\documentclass{beamer}
\usepackage{lmodern}
\usepackage[shadow,roundedcorners,customcolors]{dynblocks}
%%% Theme definitions
\usetheme{Singapore}
\usecolortheme{rose} % to have colored blocks
\setbeamertemplate{blocks}[rounded][shadow=true]
\usepackage{tikz}
\usetikzlibrary{mindmap}
% ---- from now starts code useful to draw the mindmap
%%% Overlay definitions
% based on Daniel's code
% https://tex.stackexchange.com/questions/55806/tikzpicture-in-beamer/55849#55849
\tikzset{
invisible/.style={opacity=0},
visible on/.style={alt=#1{}{invisible}},
alt/.code args={<#1>#2#3}{%
\alt<#1>{\pgfkeysalso{#2}}{\pgfkeysalso{#3}}
}
}
%%% Shadings definitions
% based on
% https://tex.stackexchange.com/questions/58249/how-to-add-shade-to-mindmap-concept/62097#62097
\makeatletter
\pgfdeclareradialshading[tikz@ball]{myball}{\pgfqpoint{5bp}{10bp}}{%
color(0bp)=(tikz@ball!30!white);
color(9bp)=(tikz@ball!75!white);
color(18bp)=(tikz@ball!90!black);
color(25bp)=(tikz@ball!70!black);
color(50bp)=(black)}
% to make possible use "myball color=..."
\tikzoption{myball color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{myball}\tikz@addmode{\tikz@mode@shadetrue}}
\pgfdeclareradialshading[tikz@ball]{myball-left}{\pgfqpoint{5bp}{-9bp}}{%
color(0bp)=(tikz@ball!30!white);
color(15bp)=(tikz@ball!75!white);
color(25bp)=(tikz@ball!90!black);
color(40bp)=(tikz@ball!70!black);
color(70bp)=(black)}
\tikzoption{myball-left color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{myball-left}\tikz@addmode{\tikz@mode@shadetrue}}
\pgfdeclareradialshading[tikz@ball]{myball-right}{\pgfqpoint{-5bp}{-9bp}}{%
color(0bp)=(tikz@ball!30!white);
color(15bp)=(tikz@ball!75!white);
color(25bp)=(tikz@ball!90!black);
color(40bp)=(tikz@ball!70!black);
color(70bp)=(black)}
\tikzoption{myball-right color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{myball-right}\tikz@addmode{\tikz@mode@shadetrue}}
\makeatother
\tikzset{level 1 concept/.append style={font=\sf, sibling angle=90,level distance = 25mm}}
\tikzset{level 2 concept/.append style={font=\sf, sibling angle=45,level distance = 16mm}}
\tikzset{level 3 concept/.append style={font=\sf, sibling angle=45,level distance = 17mm}}
\tikzset{mynode/.style={scale=0.45}}
% ---- end of code useful to draw the mindmap
\begin{document}
\begin{frame}{Title}
\begin{columns}[T]
% Figure
\begin{column}{0.49\textwidth}
\begin{tikzpicture}[mindmap, concept color=blue, font=\sf\bf, text=white,scale=0.7]
\node[mynode,circle,shading=myball,visible on=<1->]{Root Concept}[clockwise from=315]
child [concept color=orange,visible on=<2->] {node[mynode,circle, myball-left color=orange] (c1){Child 1}
child[visible on=<3->] {node [mynode,circle, myball-left color=orange](c11){Child 1-1}}
child[visible on=<3->] {node [mynode,circle,myball-left color=orange](c12){Child 1-2}}
child[visible on=<3->] {node [mynode,circle,myball-left color=orange](c13){Child 1-3}}
}
child [concept color=violet,visible on=<4->]{node [mynode,circle,myball-right color=violet](c2){Child 2}
child[visible on=<5->] {node [mynode,circle,myball-right color=violet](c21){Child 2-1}}
child[visible on=<5->] {node [mynode,circle,myball-right color=violet](c22){Child 2-2}}
child[visible on=<5->] {node [mynode,circle,myball-right color=violet](c22){Child 1-3}}
};
\end{tikzpicture}
\end{column}
% Blocks
\begin{column}{0.49\textwidth}
\begin{dynblock}
\opaqueblock<1>{
This ... consist of... because....\\
and is peculiar of...
}
\invblock<2->
\end{dynblock}
\\[2ex]
\begin{dynblock}
\setblockcolor{orange!20}
\setbordercolor{orange}
\opaqueblock<{2,3}>{
This ... consist of... because....\\
and is peculiar of...
}
\invblock<4->
\end{dynblock}
\\[2ex]
\begin{dynblock}
\setblockcolor{violet!20}
\setbordercolor{violet}
\opaqueblock<{4,5}>{
This ... consist of... because....\\
and is peculiar of...
}
\end{dynblock}
\end{column}
\end{columns}
\end{frame}
\end{document}
Result:
