I will explain how a 3D printer works, and problems that arise for people just starting.
3D printing can be explained as basically a motorized glue gun that is squirting out plastic instead of glue. It is also similar to a motorized pencil drawing in 2D. After it fills in an area, it moves up a little and starts laying plastic on top. It seems simple, and at first it is.
However, there are different kinds of things you can print in. There are different kinds of plastic, for example. There is PLA plastic, the cheaper kind, and ABS plastic, the slightly more expensive but drastically different kind.
PLA plastic is simple, and when printing with it it will print a bit rougher. It has a more plasticy feel. However, due to it's slightly lower printing temperature, it's nice (some even say candy like) and non-toxic smell, and lower amounts of warping, it is a preferred options for those using their 3D printer for printing small fun things.
ABS plastic is the same plastic as the kind used in Legos, and rounds nicer, and has a more solid feel. You can get much higher detail with this plastic, but it is a lot harder. First, unlike PLA, it has a toxic-like smell. However, while it is not poisonous, it has given a few people headaches before. The biggest problem is that it warps heavily. When warping happens, the edges start to curl up. This isn't the main problem with warping, the main problem is that less and less of the print stays is on the board. This means that it will almost always pop off and make a mess.
The solution to warping (which happens with both PLA and ABS, though not so much with PLA) is to get a heat bed. A heat bed pretty much means that the plate which prints are printed on can be heated. When it becomes hot, the bottom of the print touching the heat bed melts just a little, but enough that it stays put. Warping happens when it "dries" too fast, but with a heat bed it isn't a problem. This also means that it will stay on the bed without coming off.