The word simple has a mathematical meaning.

Def A group is said to be simple if it has no normal subgroups other than itself and the trivial subgroup.

Def A ring is said to be simple if it has no two-sided ideals other than itself and {0}.

It is used for other algebraic structures too, with an analagous meaning, whenever there is a concept of an ideal.

The Alternating group An, for n>=5, is an example of a simple group. The Weyl algebra is an example of a simple ring.