A hidden pair is the hidden single idea extended to two digits at once: if two digits, between them, can only go in the same two cells of a unit — and nowhere else in that unit — then those two cells must hold those two digits, in some order. Everything else those two cells currently list as a candidate can be crossed out.
Why it’s “hidden”
The two cells involved might still show four or five pencil marks each, which is exactly why this one gets missed. Nothing about the cells themselves looks close to solved. What gives it away is checking the digits, not the cells: if digit 4 only fits two cells in this box, and digit 9 only fits those same two cells, those two cells are locked to 9 even though they currently show more candidates than that.
Worked example
In box 8, 5 and 7 only fit in r7c5 and r8c6, so every other candidate can be cleared from those two cells.
The elimination here happens inside the pair’s own two cells, not elsewhere in the unit — the opposite of a naked pair, where the two cells stay put and everything else in the unit gets cleaned up around them.
How to find one quickly
This one’s easier to find by tracking digits than cells. For a unit that’s getting crowded, pick two digits you haven’t placed yet and count how many empty cells in that unit could still take each one. If both digits are each confined to the exact same two cells, you’ve found a hidden pair — strike every other candidate from those two cells.
Related techniques
Naked pair is the same structure seen from the other side. If pairs of either kind stop turning anything up, naked triple extends the pattern to three cells and three digits.
Puzzles at Medium are the first level built around needing this.