It's called the backbeat in rock-n-roll.

Most of us here probably do it without thinking, "Am I on the beat on or the backbeat?" A familiar song with strong backbeat opportunities is "Will the Circle Be Unbroken?". The beat is on CIR in "circle," but the rhythm or shufflebow player (s) can give a good WHUMP on that pause between Cir- and -cle.) That's the backbeat.

In folkie terms, if a band plays with shufflebow, the fiddler can take either the accented beats (ONE two THREE four) or the backbeat (one TWO three FOUR) for the invisibly-dotted notes-- while the rhythm guitar takes the other.

~Susan