When a digit's candidates inside one box all sit in the same row or column, the digit must go on that line within the box, so you can remove it from the rest of that row or column. The mirror image, box/line reduction, works the other way: if a row or column keeps a digit inside one box, remove it from the rest of that box.
Pointing pairs are usually the first thing to learn once singles run out. They don't place a number by themselves; they remove candidates, and the cleaner pencil marks often reveal a single straight away.
You will also see them called locked candidates or intersection removal. All of these names describe what happens where a box crosses a row or column.
Pointing: the box points along a line
Where the pattern lives
The pattern
Candidates removed
Solved as a result
In box 5, the 3 can only go in R4C6 and R5C6, which all lie in column 6. Whichever cell gets the 3, it uses up column 6, so the 3 can be removed from the rest of column 6: R1C6. That leaves R1C6 with only one candidate: 4.
Only the 3s are shown, so the pattern stands out.
Box/line reduction: the line claims the box
Where the pattern lives
The pattern
Candidates removed
Solved as a result
Now the other way round: in column 5, the 3 only fits in R1C5 and R2C5, all inside box 2. So box 2 gets its 3 from column 5, and the other 3s in box 2 can go: R1C6. That leaves R1C6 with only one candidate: 4.
Only the 3s are shown, so the pattern stands out.
This position comes from a puzzle generated on this site, after every single has been filled in. Boxes are numbered 1–9 from the top left, row by row; R5C4 means row 5, column 4.
How to spot it
1Pick a box and a digit that isn't placed in it yet.
2Look at where that digit's candidates are inside the box. If they all sit in one row (or one column), you have a pointing pair, or a pointing triple if there are three.
3Follow that row or column out of the box and remove the digit from every other cell along it.
4Then check the mirror image: for each row and column, if a digit's candidates all fall inside one box, remove the digit from the rest of that box.
5After each removal, look for new singles in the cells you touched.
Why it works
The box must contain the digit exactly once. If every spot left for it in the box lies on one row, then whichever spot is right, the digit sits on that row. A row can't hold the same digit twice, so no other cell in the row can have it.
Box/line reduction is the same argument with the roles swapped: the row must contain the digit once, every possible spot is inside one box, so the box's copy of the digit is already accounted for.
Common mistakes
Applying it when the digit also appears elsewhere in the box. Every candidate in the box has to be on the line; one outlier and there is no pointing pair.
Removing the digit inside the box instead of outside it. Pointing clears the line beyond the box; box/line reduction clears the box beyond the line.
Working from stale pencil marks. If a candidate should already have been removed, the pattern you see may not be real, so update the notes after every placement.
Questions
Is a pointing pair the same as a locked candidate?
Yes. "Locked candidates" covers both directions: pointing, where a box locks a digit onto a line, and box/line reduction (also called claiming), where a line locks a digit into a box.
Can there be a pointing triple?
Yes. If three candidates in a box all line up in one row or column, the logic is identical: the digit is removed from the rest of that line.
Which puzzles need pointing pairs?
Easy and medium puzzles on this site can be solved with singles alone. Pointing pairs start to matter on hard and expert grids, usually as the first step once singles dry up.
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