Succumb: To lose the will to oppose something or to give up and accept something that you first opposed. In the context of illness, to succumb to an illness is to stop opposing it, to no longer battle it, but to die from it. Succumbing, like passing, has become a euphemism (an inoffensive substitute) for dying.
As with many of our words, succumb came from Latin via France. In Latin "succumbere" means to fall down or yield. The French "succomber" crossed the Channel in the 1400s but the euphemistic sense of succumb as yielding to a disease dates only to about 1800.