Hidden pairs
The mirror image of a naked pair, and considerably harder to see — because you are looking for an absence somewhere else rather than a pattern sitting in front of you.
The idea
If two digits can each only go in the same two squares of a unit, then those two squares must hold those two digits between them. Everything else in those two squares can be erased.
Compare the two directions and the difference becomes clear. A naked pair cleans up the rest of the unit. A hidden pair cleans up the pair itself.
A worked example
Look at the top-middle box, and follow the 2 and the 7.
Across the whole box, 2 and 7 appear as candidates only in r1c4 and r1c5. Those two squares must therefore take the 2 and the 7 in some order — so the 1 and the 4 come out of r1c4, and the 5 comes out of r1c5.
Notice the shape of the argument. Nothing about r1c4 on its own suggested this; it looked like an ordinary four-candidate square. The evidence was the absence of 2 and 7 everywhere else in the box.
How to spot them
Count digits, not squares. Go through a unit asking how many squares each missing digit could occupy, and write the count down if you need to. Two digits that both answer "these same two squares" are a hidden pair.
It follows that hidden pairs are easiest to find in the unit with the fewest empty squares, because there are fewer places for the counts to be large. When a puzzle stalls, start with the most complete box.
Common mistakes
The most frequent is finding one and then erasing the wrong things — clearing the two digits from the rest of the unit, as if it were a naked pair. That is not licensed, and it will usually break the puzzle. A hidden pair only tells you about the two squares themselves.
The second is missing them entirely because the squares look crowded. A hidden pair often hides inside squares showing five or six candidates, which is exactly where the eye does not want to go.
Where to go next
The next technique in the order is pointing pairs — A digit cornered onto one line inside a box clears that line in the two neighbouring boxes.
All nine techniques: the techniques index. New to the rules? Start here. Ready to use it? Open a board.