An “apple polisher” is one who gives gifts to win friendship or special treatment. It is not exactly a bribe(贿赂), but is close to it.
All sorts of people are “apple polishers”, including politicians and people in high offices—just about everybody. Oliver Cromwell, the great English leader, offered many gifts to win the support of George Fox and his party, but failed.
There are other phrases meaning the same thing as “applepolishing”—“softsoaping” or “butteringup”. A gift is just one way to “softsoap” somebody, or to “butter him up”. Another that is just as effective is flattery, giving someone high praise—telling him how good he looks, or how well he speaks, or how talented and wise he is.