"It" as you're describing it, is about timing - you groove hard by being "on time" but not "robotic". A bassist and drummer who groove hard (it takes 2 to tango) understand, without having to discuss it, where to push and pull the beat - if the drummer is doing syncopated stuff, you put down a parade of dead on the beat quarter notes, so the syncopation stands out, and the rest of the band knows where the beat is. If you're pushing and pulling on the beat to deepen the groove, he's holding down the precise timing for you - it's a give and take thing (a rhythmic dance, really) that happens more or less automatically between two really good players.
Last weekend, I was playing with a less experienced drummer - she was decent, but when I pushed or pulled on the beat, she didn't dance - she followed me - I realized I had to play much straighter, or we'd wander off tempo. We (regardless of my experience) didn't have "it". Over time, maybe, but as of this point, not there. This weekend, the drummer I'm playing with - we're good. We'll have "it".
How do you get here? First off, you have to be able to play right on the beat - practicing with something with good timing helps here, whether it's tunes, a metronome, or whatever. The more precise you can be, the better - if you want to push and pull on the beat, you have to know where (actually when) the beat is. The rest is experience - it isn't going to happen the first time you play out somewhere, but if you play out enough (hundreds of gigs), and are paying attention, it's a skill that organically gets built.