I want to create a box (in which I put extra information for the reader) that behaves like a float. In other words, it should have a caption (outside of the box that says Box 1: Here is my box caption) and label that I can refer to with \cref like any other float.
Most of the solutions using \fbox, \framebox, \usepackage{framed} are all creating the box, but not about the caption and the label.
How to accomplish a floating box?

\captionofmacro from thecaptionpackage. However, there is no reason you can't put a box around the content of a float figure. – Steven B. Segletes Apr 27 '16 at 01:36\captionofhas aboxoption? (It does not from my experimentation). I want the caption to sayBox 1: blah, and ideally, the\creffrom thecrefpackage to intelligently refer to the float as aBox. – Heisenberg Apr 27 '16 at 01:39