"recovering strength and health after sickness," 1650s, from French convalescent, from Latin convalescentem (nominative convalescens), present participle of convalescere "thrive, regain health, begin to grow strong or well," from assimilated form of com-, here probably an intensive prefix (see com-), + valescere "to begin to grow strong," inchoative of valere "to be strong" (from PIE root *wal- "to be strong").
As a noun, "one who is recovering strength and health after sickness or debility," attested from 1758.