A relapse (etymologically, "who falls again") occurs when a person is affected again by a condition that affected them in the past. This could be a medical or psychological condition such as depression, bipolar disorder, multiple sclerosis, cancer or an addiction to a drug.
For example, if someone who had problems with alcohol were to give up alcohol and then later start drinking again, this drinking might be considered a relapse. It is different from a slip or lapse in that it implies a return to previous behaviour patterns, as opposed to a one-time occurrence.
It may also, in medicine, mean the end of a remission.