to do something to change, reduce or remove the bad effect of something
The new benefit is intended to compensate for the lost opportunity costs associated with homemaking.
to do something to change, reduce or remove the effects of a personal fault, injury or weakness etc
His weakness on his left hand side doesn't really stop him from doing anything because he compensates with his right side, where he is strong.
to give someone money or some other form of payment to make up for a loss or an injury
The Ministry of Defence says it compensates when liability is proven, but argued that the claims have come too long after events.