1. The definition of "pocket playing" from the words of Dennis Chambers.
"When Dennis first joined P-Funk, George Clinton didn't want him to play directly on the click, he wanted it a little behind, just so it lagged a little but was still in time. Thus, the term he coined was play it "in the pocket".
And
2. "Regardless the setting you’re in, what genre of music you’re playing or the instrument you play in, what you’re playing has a “musical center” that is referred to as the pocket. In essence, the music is centered. Nothing is moving ahead of anything else or behind anything else; everything is moving along together.
"“Generally, the pocket is the perfect synchronicity of the bass drum and the bass guitar. When applied to an entire band, it’s about everyone playing in perfect time, with attitude...
I like George Clinton's explanation best. Playing slightly behind the beat has particular importance (in some cases) for the bassist, because the attack of bass notes tend to have a longer delay -- from no sound to maximum sound -- than on other instruments. Also, some speakers react slower than other. If you are working with speakers that react slowly (especially during the time of Clinton), then a bass player would have to play before the beat so that when the down beat finally occurs, the bass sound is has reached its maximum volume.
I remember when I was in high school band, tuba players were taught to play slightly before the beat for the same reason: if they articulated on the beat, the sounding note would feel ahead of the beat, and since the bass has to support the harmonies, it's crucial to have it sounding on the beat.
Also, there's a certain feel to a rhythm that has instruments articulating the beat at slightly different times while maintaining the tempo. Blues, jazz, and funk, are only a few examples. One that I think of a lot is the rapping of Snoop Doggy Dogg in the 90s (not Lion). When you hear him rap, he has a "laid back" style. He tends to rap slightly behind the beat, but he is never out of time. That's a particular style that I've noticed in him.
So if the second definition, as the music as "centered" means anything, it means that everyone is in the same tempo, but perhaps not everyone is articulating it at the exact same moment. So in a way, the second definition is no definition at all: "centered" just means "in tempo" (not speeding up or falling behind (overall, though perhaps there can be that from measure to measure while still being "in tempo" (where "out-of-tempo" would mean a complete disaster with regard to tempo and cause gross poly-tempos (though that could be cool if that's what you're into)))). To create "the perfect synchronicity of the bass drum and the bass guitar," the bass would have to play slightly behind the kick so that the kick articulates the attack of the bass as it ramps up to its maximum volume.
"In the pocket" then would mean to play slightly behind the drums.
If my assertion is correct, that it has to do with the attack of the electric bass that requires the metaphor "in the pocket," and that playing the behind the beat was more crucial at a time when many speakers articulated slower than others, perhaps many faster-articulating speakers would make a bass player play less behind the beat to achieve the best pocket positioning.