COINTELPRO is some kind of military term because of COIN that has to do with counter insurgency.
No, COINTELPRO was a Cold War era FBI covert operations program in which the FBI carried out illegal surveillance, infiltration, harassment, and misinformation programs against domestic political organizations deemed "subversive" by J. Edgar Hoover (which was pretty much everyone he didn't like, including the entire civil rights movement). And no, this wasn't "illegal as in left wing people don't like it", it ran the gamut from surveillance without legally required warrants to falsifying evidence.
(There is a fairly infamous letter from J. Edgar Hoover himself to an FBI agent who had investigated the local Black Panther Party as part of COINTELPRO and found that it
wasn't doing anything illegal and that its primary activity was a breakfast program for schoolchildren. Hoover was enraged by this finding and quite explicitly threatened to ruin the agent's career unless he "found" evidence that the Black Panthers were a violent terrorist organization as Hoover believed.)
While the program was officially terminated in 1971, the term remains in use as something of a generic term for the belief that the government still runs programs like that.