Snap Cap brand dummy rounds are designed to cushion the firing pin on recoil. They will not cycle the gun. In other words, if you have a striker fired gun, you will have to rack the slide each time you dry fire (ejecting the round in the process).
Most modern centerfire guns can be dry fired without snap caps (don't do it to most rimfire guns, however). If your manual says not to dry fire, then use snap caps. Dummy rounds have other uses too, though I wouldn't buy snap caps, simply because they're usually more expensive than other dummy rounds.
Sticking dummy rounds randomly in a magazine with live ammo while at the range can do two things for you. One, it can diagnose a flinch (if you anticipate the shot, your hand will move to anticipate the recoil...doing this during live fire will make you miss your target). Two, it gives you the opportunity to practice a malfunction drill (tap, rack, bang).
You can also use them to set up a double feed (which you can do with empty brass, or even live ammo if you're at a range) to practice clearing that malfunction. I sometimes use those to set up malfunction drills at home.
Another use, that I use them for is practicing reloads during my dryfire practice. Having dummy rounds in the magazine makes the gun act like it has ammo. Since I don't use the slide release (and instead use the rack method) during a slide lock reload, using an empty magazine won't allow me to release the slide properly.
Snap caps, or dummy rounds are very useful, and I'd recommend having some jsut for what I've said above. But they really don't do anything special. People who reload ammo make dummy rounds for their personal use all the time (just make sure they are painted or something to show they are INERT.