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Many of those class's abilities award a combo point (hence the name) when performed, which are marked on the target and can stack up to 5 points. Changing target does not make you lose your combo points, however performing a combo awarding ability on the new target does wipe out the points you had on the old target.
Combo points are use to fuel finishers. While combo awarding abilities are usually pretty straightforward damage dealing abilities, finishers are usually much more versatile. The more combo points you have, the more powerful the finisher will be.