Power Truncation, in a method which considers pairwise opposition, means that for every pair of candidates a and b truncated (not ranked) on a given ballot, a full vote of opposition is scored for each over the other, with the goal being to increase the maximum opposition sustained by those candidates even more than a random ordering would. Power Truncation could be an option that the voter may choose to use, or it could be built into a method's rules that this is how truncation is treated.
With a pairwise-count method, when a voter chooses the power truncation option, that means that s/he wants, for any candidate s/he doesn't rank, that his/her ballot be counted as voting every one of the other candidates against that one.
So every candidate s/he doesn't rank is treated as if it were last-ranked on his-her ballot, with all the others ranked over that candidate.
Mike Ossipoff proposed and named this option. It was thought mainly to be usable with Minmax (pairwise opposition) specifically.