You try to lift up your young child by his/her arms. You may or may not hear or feel a pop. Suddenly, your child's arm is kept straight, and your child doesn't move it much. You child may or may not cry in pain... Congratulations! You've just caused nursemaid's elbow.
A rather common affliction in small children, it's named due to the fact that anyone taking care of a young child may be prone to causing it. Though commonly thought to be a dislocation of the elbow, what really happens is that a chunk of ligament or synovium gets stuck somewhere between the heads of the bones in the elbow.
If you're not squeamish, and confident in your ability to not cause irreparable harm to your child's arms, you can fix this yourself. Have a pediatrician teach you. A quick, gentle pull, a twist, and bending of the arm usually fixes it right up. In the worst case scenario, little junior ends up with a cast for a few weeks.
I just spent three hours in the ER last night, waiting to see a pediatrician who was able to fix it in under a minute... but potentially, it could have been something worse, so nothing bad about going to the ER when you have to...
The irony is that my wife is an M.D., but she's a pathologist so it's not too ironic...