No one really answered your question about what they are. They mount between the rim and the axle hub. This moves the rim and tire further away from the center of the vehicle. You get a wider stance (which can be accomplished with a lower Backspacing, as already mentioned).
When will you need them? If you have a set of rims that you want to put on, but they won't clear the break calipers (mostly 15"). You can add the spacers to move the rim further from the caliper.
You can also add them to get a wider stance for stability, or the appearance (again, you can do this with different rims too).
They may or may not allow you to fit a tire that you could not otherwise fit. Probably not since it would rub other places.
Problems? They add a little extra stress on the suspension (but so does low backspace rims). They can also corrode if you get cheap ones (spidertrax are anodized, so less of an issue). And as mentioned, there are more lugnuts to be concerned with. I've never heard of one falling off though. I may add some myself, but my main concern is the fact that your lug studs would be mounted in aluminum instead of steel. Your original studs are used to hold the spacer on and the lug studs mounted in the spacer (aluminum) hold the rim on. Not a fan of a block of aluminum holding my rim on...
Rescu2000
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2003 Liberty Sport 4X4
DIY Frankie Lift, BBS Rims, Aussie Locker Rear, DTT Front, Renegade Rack & Light Bar, Custom Front Bumper w/ Warn XD9000i, Custom Rear Bumper, JBA UCA's, Full Skids(Mopar, Kilby and Super skid), CRS Rock Rails, CB, EVIC, Nav, power dim mirror, (2) 8" subs under front seats.
http://www.cardomain.com/ride/2512777