Regular gems are only useful for selling/trading with. There are a couple special gem types (in act 4), but it should be obvious from the context that they are different (and I'm pretty sure you can not sell them).
The crystal bag holds crystals, which give you a resistance boost (when put in the bag). You can mix and match crystals to give you a higher resistance against the type of damage creatures do in the area you are in, or just load the bag up with the largest crystals you have.
