Where can I find "aligned" environment documentation?

The aligned environment is from the amsmath package, and as such the documentation of amsmath is the first place to look. As David says, most users will have the documentation of the packages installed with their TeX distribution, so you can execute

texdoc amsmath

in a terminal/command prompt to open amsldoc.pdf.

The description of aligned (and gathered, alignedat) is found in section 3.7 Alignment building blocks, which start on the bottom of page 7. On the middle of page 8, the optional arguments to these environments are described:

Like the array environment, these -ed variants also take an optional [t] or [b] argument to specify vertical positioning.

A quick example demonstrating the difference:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Text $\begin{aligned} a \\ b \\ c \end{aligned}$ text
$\begin{aligned}[b] a \\ b \\ c \end{aligned}$ text
$\begin{aligned}[t] a \\ b \\ c \end{aligned}$ text.
\end{document}