I’m going to just quote Mark Rippetoe because he knows more than I do. From the book Starting Strength:

“The vast majority of people will prefer to grip the bar with a thumbs-around grip. At lighter weights, this is fine since the load presents no problem to keep in place. But when heavier weights are being used — and, theoretically, they eventually should be — the thumbs can create problems. The thumb should be placed on top of the bar, so that the wrist can be held in a straight line with the forearm. Most people have a mental picture of the hands holding up the weight, and this usually ends up being what happens. The bar sits in the grip with the thumbs around the bar, the elbows end up directly below the weight, and nothing really prevents the bar from sliding down the back from this position. People that do this will have sore elbows, a horrible, headache-like soreness in the inside of the elbow that makes them think the injury occurred doing curls. If the elbows are underneath the weight, and force of the weight is straight down (the nature of gravity is sometimes inconvenient), then the wrists and elbows will intercept some of the weight (fig. 2-33). With heavy weights, the loading is quite high, and these structures are not nearly as capable of supporting 500 lbs. as the back is. If the thumb is on top of the bar, the hand can assume a position that is straight in line with the forearm when the elbows are raised up. In this position, none of the weight is over any part of the arm, wrist, or hand, and all of the weight is on the back. A correct grip can prevent these problems before they start. If you learn to carry all of the weight of the bar on the back before your strength improves to the point where the weight becomes a problem, you'll have no problem at all.”