It isn't clear from your posting whether you're trying to understand:
- Why the inequalities generated by the Sherali-Adams procedure are valid?
or
- Why the procedure is complete in the sense that after enough iterations you arrive at the convex hull of the integer solutions of the original integer linear programming problem?
I suppose that you might also be interested in the question of how this can be used in practice.
You should be aware that Sherali-Adams is just one of several "lift and project" schemes based on LP or SDP relaxations that provide a ladder of relaxations of an integer programming problem from the simple LP relaxation up to a relaxation that has only integer solutions as its extreme points.
You might find the following paper by Monique Laurent to be useful in understanding this stuff:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.2521