Your best bet is to read up on them in your Jeppeson Instrument/ Commercial textbook or Instrument Flying Handbook (FAA).

DME arcs are drawn at certain distances around VORs and occasionally other navaids, to serve as a flexible IAF to an approach. They once were only VOR-based but now GPS has them. DME arcs are often used with back course approaches. BC approaches are simply the opposite side of a typical localizer. BC approaches makes two approaches from one localizer, saving the taxpayer some money. Just make sure you engage the "BC" button the autopilot, if you are using one that does not know which way the approach is being flown front or back. Older Bendix Kings and S-Tecs are what I have in mind, but I think they all need to be set for back course localizer even on the G1000/ GFC700 autopilots.

The nice thing about DME arcs is that they can be intercepted at any angle. This saves time and makes the approach more efficient because you have an almost unlimited number of initial approach fixes. They can be a bit challenging to track with only one VOR receiver and DME, but it gets easier with two VORs plus DME, and it becomes a no brainer with gps.