Like many surnames, it is probably based on the geographical area in which the original holders of the name lived. 'Brecken' is possibly a variant of 'broken' and 'ridge' - from Old English 'ryg' - meant a raised piece of ground. So, the 'Brokenridges' - later Breckenridges - were probably the family who lived on a hillside close to where there was a a gap/break/valley in it.
Despite the one-starring, I'll still offer you another couple of options. It could have referred to a ridge covered with bracken and, in addition, Bracca was a personal name in Old English times. Thus, the ridge concerned might have been one that belonged to a local bigwig with that very name. It's easy enough to see how Brackenridge or Bracca's Ridge - as well as Broken Ridge - became Bre(c)kenridge over time. (I hope you find an answer you actually like!)