meaning of giving substance

If you "give substance" to something, you obviously add to it something that one might call "substance".

This can be the generic meaning of "substance", meaning any sort of tangible material -- dirt, salt, sulfur, steel -- or it can be figurative "substance", meaning that something (such as a theory) which originally was "insubstantial" (eg, lacking evidence as to its validity) is "given" a property (eg, evidence to support it) that makes the theory (more) "substantial".

You may see the idiom used in a number of different contexts: Leaked emails "give substance" to accusations of malfeasance on the part of some public official, test results "give substance" to a company's claim that it has solved the fission energy problem, an amazing performance on the part of an actor "gives substance" to the claims that he's the next Laurence Olivier.