Finesse is when you persuade someone to do something to your liking. Though there's no proof of where the term started, many claim that the term finesse started in Chicago, Illinois. Finesse is a slang term heavily used in Hip Hop music by rappers, it became widely popular due to its heavy use in Drill Music. Speaker Knockerz is also credited for the rise of the term finesse; he had a mixtape titled "Finesse Father." Though it may look like you robbed someone after finessing them, finessing is not the same thing as stealing.
Migos said the following in their song China Town: "I got the birds singing like I'm Richie Lionel, I mean Lionel Richie - Finessing the plug, again I did it." Migos is basically saying their drugs are moving fast, and he managed to talk his dealer into selling it at a discount, or giving it to him for free (highly unlikely).
"Finnessed her out of her panties" means you talked a girl into having sex with you.