A pair is a set of two things that go together. In cubing this most often refers to two pieces that are adjacent to each other when the cube is in a solved state. Pairs are most commonly used in any LBL that solves the first two layers together (F2L), like the Fridrich Method. A corner and a edge is paired to form a 'CE pair' that then is placed into position. In the Reduction Method edges are paired up and becomes dedges. Uncommonly it may be any two adjacent pieces on any puzzle.
Pairs can sometimes be considered a primitive form of blockbuilding.
To pair, pair up; (verb), the actual forming of a pair of pieces, achieved by twisting the sides and/or slices of the puzzle.