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 aligned
and gathered
are intended for use within other math environments, such as the normal \[ ... \]
or the equation
environment. Their counterparts align
and gather
are displayed math environments in their own right, and should not be used within other math constructs. align
and gather
will number each line, but have also got unnumbered versions, align*
and gather*
. The unnumbered versions are used by default in LyX when you do Insert --> Math --> AMS Align/Gather.
gathered
.aligned
. I'll write an answer of sorts.