What's the difference between align and align*?

The star at the end of the name of a displayed math environment causes that the formula lines won't be numbered. Otherwise they would automatically get a number.

You can read about that in the amsmath user's guide since align belongs to amsmath.

Such information can usually be found in the package documentation. Type texdoc packagename at the command prompt or visit http://ctan.org/pkg/packagename. If you use google or another search engine, look for starred and commandname.

Commonly, a star symbol * means a version of a command that behaves differently from the original. That often means suppressing numbering but could also refer to special features. For example, have a look at What's the difference between \newcommand and \newcommand*?

"One could take a look in the manual out of sheer desperation." (based on Herbert Voß)

Googling should have told you that align and align* are part of the amsmath package. Page 3 of its documentation reveals:

The amsmath package provides a number of additional displayed equation structures beyond the ones provided in basic LaTeX. The augmented set includes:

[...] align align* [...]

Except for split, each environment has both starred and unstarred forms, where the unstarred forms have automatic numbering using LaTeX’s equation counter.

You could also simply try out what the difference might be:

\documentclass{article}

\usepackage{amsmath}

\begin{document}

\begin{align}
a_1& =b_1+c_1\\
a_2& =b_2+c_2-d_2+e_2
\end{align}

\begin{align*}
a_1& =b_1+c_1\\
a_2& =b_2+c_2-d_2+e_2
\end{align*}

\end{document}