electron correlation
Imagine a crowded dance floor where everyone has the same magnet sewn into their shirt, pushing all the dancers apart. Nobody can move thoughtlessly: each step you take depends on where everyone else is, because you're all constantly dodging one another. The dancers' movements become linked, or correlated — you can't describe one without watching the rest.
Electrons inside a material do exactly this. They all carry negative charge, so they all repel one another, and an electron will subtly steer its path to stay away from the others. Electron correlation is precisely this coordinated dodging: the chance of finding one electron somewhere is changed by where the other electrons happen to be. The simplest theories pretend each electron moves on its own through an average smear of all the others; correlation is everything those theories leave out.
It matters because correlation is behind some of the strangest and most useful behavior in materials, from magnetism to certain insulators that 'should' conduct, and possibly high-temperature superconductivity. The honest caveat: in many ordinary metals correlation is mild and the simple average picture works surprisingly well, so the word usually flags the harder cases where that picture breaks down.
In a helium atom, two electrons orbit the same tiny nucleus. They never sit on opposite sides by accident — they actively stay apart, like two people circling a small table so as not to bump. Accounting for this mutual avoidance changes the atom's measured energy by a few percent, a discrepancy that puzzled early quantum physicists until they named it correlation.
Two electrons in a helium atom keep apart on purpose — that mutual dodging is correlation.
Physicists use 'correlation' narrowly: it means the part of the electron interaction left over after you've already accounted for the average repulsion and a quantum effect called exchange. So 'no correlation' doesn't mean 'no interaction' — it means the leftover, hard part happens to be small.