This type of bar may be called a trap bar (because it works your trap muscles on the top of your shoulders when doing shrugs), hex bar, or shrug bar. It's mainly used for deadlifts or shrugs. Originally it was called a diamond deadlift bar, due to its shape.
For the deadlift, this specialized bar gives the ability to keep your hands at your sides and nearly eliminating the risk of hitting your legs like you would with a conventional deadlift with a straight bar. This makes the lifts less technical to perform, allowing you to increase the weight substantially and reduce the risk of a back injury due to poor form.
See our blog post: Buying a Hex Deadlift Bar: High or Low Handles?