A farkle is when you can't score because you either don't have enough points to bank.
In other words...say you need 250 points to bank.
You roll a 2, 3, 1, 5, 5, 2. You can count the 1 (100 points) and the two 5s (2 @ 50 = 100 points). You have 200 points but you can't bank them yet as you're 50 points short. So you roll the remaining dice and come up with a 2, 4, 6. You can't count those three toward your bank, so you end up getting a Farkle. If that happens 3 times in a row, you lose a 1000 points.
It may sound confusing, but it's not that hard to figure out how to play it. However, you can see it in action if you're on Facebook. Search for Farkle and play it a couple of times. The game can be addicting.