Many of amsmath environments are already in math mode.
This applies to the environments
equation,
align,
gather,
flalgin,
alignat and
multline
as well as their starred (unnumbered) versions.
The environment split is to be used inside amsmath environments and can be used to split one equation on more than one line (this important for the equation number).
The environments
aligned,
gathered and
alignedat
are similar to the version without -ed but are to be used in math mode.
As pointed out in the comments by Torbjørn T. empty lines aren’t allowed in math mode, they trigger the same error message.
amsmath’s environments (those who actually enter math mode) center their contents horizontally. The align family aligns its content internally at every odd &. See the example below how they work. You can use the fleqn option so that amsmath align the whole content of its environment at the left border (with a certain margin).
Code
\documentclass{article}
\usepackage{amsmath}
\usepackage{showframe}
\begin{document}
\begin{equation}
c^2 = a^2 + b^2
\end{equation}
\begin{gather}
c^2 = a^2 + b^2 \\
a^2 + 2ab + b^2 = (a + b)^2
\end{gather}
\begin{align}
\text{right-aligned} & \neq \text{left-aligned} \nonumber\\
c^2 & = a^2 + b^2 \\
a^2 + 2ab + b^2 & = (a + b)^2
\end{align}
\begin{align}
c^2 & = a^2 + b^2 \\
\begin{split}
a^2 + 2ab + b^2 & = (a + b)^2 \\
& = (a + b)(a + b) \\
& = aa + ab + ba + bb \\
& = a^2 + 2ab + b^2
\end{split}
\end{align}
\end{document}
Output

alignis automatically in math-mode. No need to enter it manually. Remove the$. – Qrrbrbirlbel Aug 14 '13 at 18:03alignenvironment already switches to math mode; the$are for inline math-mode. – Corentin Aug 14 '13 at 18:04alignaren't allowed, I believe. – Torbjørn T. Aug 14 '13 at 18:04