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1.
(Scots Vernacular) The removing of one's shirt or other upper body garments, most often in the event of warm weather but also often for purposes of celebration or simple antagonism.
Lt Data: "Captain, due to our proximity to this binary star, hull temperature has already reached critical levels and internal sensors indicate imminent failure in the enterprise's internal cooling system"

Captain Jean-Luc Picard "Right every c*nt, taps aff"
by I Hate The Future April 30, 2012
 
2.
Glaswegian (Scottish). Literally "tops off." Originally an expression for hot weather, hot enough to take one's shirt off. A phenomenon rarely seen in Glasgow. Now an expression describing good times being had. Often issued as an instruction.

The lesser-used opposite would be "taps oan."
Ah'm pure sweatin' buckets, man. Taps aff!
by Big McWeesmall July 24, 2012