Middle English mēten, from Old English metan "to find, find out; fall in with, encounter, come into the same place with; obtain," from Proto-Germanic *motjanan (source also of Old Norse mæta, Old Frisian meta, Old Saxon motian "to meet," Gothic gamotijan), from PIE root *mod- "to meet, assemble." Related to Old English gemot "meeting."
By c. 1300, of things, "to come into physical contact with, join by touching or uniting with;" also, of persons, "come together by approaching from the opposite direction; come into collision with, combat." Abstractly, "to come upon, encounter (as in meet with approval, meet one's destiny) by late 14c. Sense of "come into conformity with, be or act in agreement with" (as in meet expectations) is by 1690s.
Intransitive sense, of people, "to come together" is from mid-14c.; of members of an organized body or society, "to assemble," by 1520s. Related: Met; meeting. To meet (someone) halfway in the figurative sense "make mutual and equal concessions to" is from 1620s. Well met as a salutation of compliment is by mid-15c.