There are different types of rehabilitation, so it really depends on what type you are referring to. In general, it is the time spent correcting an issue. For instance, there is drug or alcohol rehabilitation where people spend time recovering from substance abuse and learning how to cope without needing those substances. There is also physical rehabilitation that is used for those who have sustained injuries of some sort and need to strengthen their muscles or learn how to properly move without further damaging their bodies.
Convalescing refers to the elderely or a gradual return to health maybe after a surgery. You can convalese in a nursing home or a rehabilatation facility.