ASS stands for "angle-side-side".
It is also abbreviated as SSA (for "side-side-angle"), but it
is easier to remember it as ASS, which is also a donkey and has
implications of stupidity.
There are two triangles, ABC and DEF. We are given that side AC is congruent to side DF, angle A is congruent to angle D, and side BC is congruent to side EF. Notice that the congruent angles are not included between the congruent sides. This is very important.
These conditions do not imply that the two triangles are congruent, as can be seen in the diagram.
If the congruent angles were included between the congruent sides, then we would have SAS, which is a postulate. But when it is not, then we could have two different triangles, which are not at all congruent.