It's just a way to have more than one VOR approach to the same runway. Often the VOR/DME 1 RWY 22 (as an example) will be a simple teardrop or procedure turn approach, and the VOR/DME 2 RWY 22 will be a DME arc with several transitions off of different airways. It just provides more options in cases where they can't combine the two procedures into one approach.