1520s, "pertaining to the celestial tropics," from tropic + -al (1). In reference to the torrid zones of the earth, from 1690s. Meaning "hot and lush like the climate of the tropics" is first attested 1834.
late 14c., "either of the two circles in the celestial sphere which describe the northernmost and southernmost points of the ecliptic," from Late Latin tropicus "of or pertaining to the solstice" (as a noun, "one of the tropics"), from Latin tropicus "pertaining to a turn," from Greek tropikos "of or pertaining to a turn or change; of or pertaining to the solstice" (as a noun, "the solstice," short for tropikos kyklos), from trope "a turning" (from PIE root *trep- "to turn").
The notion is of the point at which the sun "turns back" after reaching its northernmost or southernmost point in the sky. Extended 1520s to the corresponding latitudes on the earth's surface (23 degrees 28 minutes north and south); meaning "region between the tropics of Cancer and Capricorn" is from 1837.