Definition of connectors
In poker, connectors are cards that follow each other. 2-3, 3-4, 6-7 are connectors. There are two types of connectors; matching connectors (e.g. 5-6 of hearts or 5-6 of spades, etc) and unmatched connectors (5 of spades, 6 of hearts). The matched connectors have on average an extra 5% equity over the unmatched connectors, which is not negligible.
The playability of connectors
Connectors, especially suited connectors, are very popular as a starting hand among poker players. One of their greatest strengths is their playability. Even though a hand like A2 has a higher absolute value than a hand like 9-10 in hearts, a hand like 9-10 in hearts will have better playability. When a hand has more playability, it will be more successful in the long run. If you have the initiative and a matching connector, there are few flops you won't bet on. Matching connectors give us good reasons to bet. For example, if with flop 9-10 in heart you see a flop like 7-8-2 with a single heart. You would bet in position with your draw. Your opponent might fold to leave you the pot. But even if he calls, a 2nd heart on the turn will give you another reason to bet. You are betting here to maximize your fold equity and because your hand has just gained equity.