1) Forced Error- A forced error is when your opponent hits a really good shot (powerful groundstroke, angled volley, drop shot, lob, etc), that you have to run, stretch, dive or scramble to get. Once you get there you are unable to put it back into the court or you hit the net. Technically, you made a mistake but since the your opponents hit a superior shot, they "forced" that error. Basically, if you hit a shot on the run and it doesn't go in, it's a forced error.
2) Unforced Error- An unforced error is a mistake that you make due to simply hitting the ball incorrectly (shanks, mishits) or using improper positioning, lack of precision or just bad luck (such as hitting the let cord and having it drop back on your side). In other words, if you are playing a neutral rally and your shot goes out of bounds or hits the net, that is an unforced error.
Double faults are also considered unforced errors in some tournaments and "service winners" (unreturnble serves that are not deemed aces because the opponent touched it) can also be considered forced errors.