Compensate is about correcting for an imbalance. If you step in an unmarked pothole, the city may compensate you by paying your doctor bills treating a broken ankle.
Compensate can also mean "to adjust for." So, if you did stumble into the pothole and injure your left leg, then you might compensate by leaning heavily on your right leg. Increasingly, compensate is used in place of pay. Day laborers are paid for their time, but executives are more likely to be compensated with a suite that includes salary and other benefits––what is commonly referred to as a compensation package.