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1.
v. to show respect, often used in the imperative tense.

This phrase originated as a result of the protocols observed during audiences with the catholic pope. At the close of the audience, the subordinate would traditionally show his respect to the leader of the church by kissing the papal sigil ring.
"I've got a 2pm meeting with the boss... but I'm not about to kiss the rings."

"You just got crushed 49-0 in Madden-- kiss the rings, bitch!"
by Master Control April 22, 2007
 
2.
Euphemism for licking or kissing the rectal opening. Historical reference includes kissing the king's hand as a tribute or gesture of thanks, in return for being granted special access or position.
"We won't be allowed to do this until we 'kiss the ring'"
by wowallthegoodnamesaretaken August 30, 2011