One normal usecase of
aligned is to align certain elements, typically the (in)equality signs, of the different lines while having a single equation number for the whole set. (As opposed to numbering each line separately.)
aligned is basically a tabular structure where the columns are aligned as
rlrlrlrl.... That is, the first, third etc. columns are right aligned, the second, fourth etc. are left aligned. To align equations by the equals sign, put the left hand side of the equations in the first column of the
aligned, the equals sign and the right hand side in the second column. (The
= should not be in the first column, the spacing will be wrong.)
In LyX, when you do Insert --> Math --> Aligned environment, LyX adds two columns, indicated by the two blue boxes:
To write something left aligned, put it in the second of these two boxes. To add new columns you click the New column button -- -- on the Table toolbar (usually found on the bottom of the LyX window).
If you don't need any alignment, use
gathered instead, which just centres the lines.
Note that both
gathered are intended for use within other math environments, such as the normal
\[ ... \] or the
equation environment. Their counterparts
gather are displayed math environments in their own right, and should not be used within other math constructs.
gather will number each line, but have also got unnumbered versions,
gather*. The unnumbered versions are used by default in LyX when you do Insert --> Math --> AMS Align/Gather.