Amp stands provide isolation. Many people do find that they make a difference. Their goal is to decouple the amp from the floor so that vibrations from your speakers don't introduce vibrations into the equipment. It's no different than isolating your CD transport or turntable. Seems to me that it would be more effective for tube equipment than SS, but alot of people get good results with SS amps too. The stands are designed to not resonate and provide good ventilation.
You can make a decent nonresonant stand using concrete paving slabs, a tube of liquid nails, and sand. Then use cones between the platform/amp and platform/floor interfaces. Marble and granite look nice, but I've read complaints about them being resonant. You want a completely dead platform on which to rest your amp. Some people like maple or some exotic dense woods.
If you have a couple of weeks to get lost reading web posts, do a search in audioasylum and there you will find a lot of discussion about amp stands and isolation. Depending on the gear that you have, an amp stand may not make an audible difference or you may already have a fairly dead platform.