A groove is an indentation or rut in something — like the grooves on an old record.
Groove is rooted in an old Dutch word for "furrow" or "ditch." And that's just what a groove is: a carved out line, like wheel ruts in a muddy road or the narrow opening that a sliding door moves in. If you can't "find your groove," you feel off track and out of whack. But when you're "in the groove," everything is working smoothly and you've found a good routine. And if someone says "let's groove!", they want to dance.