As you know, the general idea behind an indirect argument is to start with a certain assumption P, and deduce (obtain validly) from it a conclusion Q which cannot be true. Then, the assumption P must be false, otherwise Q would have to be true and it isn't.

Let A be the argument
P1
P2
.
.
Pn
----
C

If A is invalid, then it is possible for P1...Pn to be true and C false (by the definition of validity). That is, there is a possible world (a possible scenario, a row in the truth table) W that makes P1,..Pn, -C true. Now, from P1,...Pn, -C we derive (i.e., obtain by a valid argument) a contradiction. A contradiction is a statement S of the form A&-A, and it is false in all possible worlds (there's no row in which it comes out true), including W. Hence, W makes P1,...Pn, -C true and S false. But this cannot be, because in a valid argument it's impossible for the premises to be true and the conclusion false (there's no possible world W, no row in the truth table, that makes the premises true and the conclusion false). So, such a world W is not possible, and therefore A is valid.