mid-14c., in chess, said of a king when it is in check and cannot escape it, from Old French eschec mat (Modern French échec et mat), which (with Spanish jaque y mate, Italian scacco-matto) is from Arabic shah mat "the king died" (see check (n.1)), which according to Barnhart is a misinterpretation of Persian mat "be astonished" as mata "to die," mat "he is dead." Hence Persian shah mat, if it is the ultimate source of the word, would be literally "the king is left helpless, the king is stumped."
word-forming element of Greek origin meaning 1. "after, behind; among, between," 2. "changed, altered," 3. "higher, beyond;" from Greek meta (prep.) "in the midst of; in common with; by means of; between; in pursuit or quest of; after, next after, behind," in compounds most often meaning "change" of place, condition, etc. This is from PIE *me- "in the middle" (source also of German mit, Gothic miþ, Old English mið "with, together with, among").
The notion of "changing places with" probably led to the senses of "change of place, order, or nature," which was a principal meaning of the Greek word when used as a prefix (but it also denoted "community, participation; in common with; pursuing").
The third, modern, sense, "higher than, transcending, overarching, dealing with the most fundamental matters of," is due to misinterpretation of metaphysics (q.v.) as "science of that which transcends the physical." This has led to a prodigious erroneous extension in modern usage, with meta- affixed to the names of other sciences and disciplines, especially in the academic jargon of literary criticism: Metalanguage (1936) "a language which supplies terms for the analysis of an 'object' language;" metalinguistics (by 1949); metahistory (1957), metacommunication, etc.