A connected pair is a pair of candidates for which we have established that they cannot be false at the same time.
Connected pairs are formed by solving techniques like coloring, XY-Wing and several types of chains. Because they cannot be false together, at least one of them must be true. This often allows us to eliminate candidates that can see both ends of the connected pair.
Do not confuse them with conjugate pairs, in which only one of the candidates can be true. A conjugate pair satisfies the definition of a connected pair, but it is not possible to use a connected pair as a conjugate pair.