Claiming
Claiming happens when every candidate for a digit inside a row or column sits inside a single 3×3 box. The row or column has to contain that digit somewhere, so it must live in one of those in-box cells — which means the rest of that box can't have it. You get to cross the digit off every other cell in the box.
What is Claiming?
Claiming — sometimes called line-box reduction — is the mirror image of Pointing, and usually one of the first intersection techniques you meet after singles. The setup: inside one row or column, all the pencil-mark candidates for a particular digit fall inside a single 3×3 box. That box is now claimed by the line for that digit, so any other candidate for it inside the box, off the source line, is dead. Regular Claiming only does the elimination — it doesn't check whether a placement falls out of it. That extra step is what Direct Claiming adds.
How to spot it
Scan the rows and columns one at a time and look for a digit whose candidates all cluster inside one box. With pencil marks on, this jumps out — the marks for that digit bunch into a single 3×3 area instead of stretching along the line. Once you see it, sweep the rest of that box and erase the digit wherever it appears outside the source row or column. Claiming shows up a lot in the first half of a solve, when the grid is still crowded with candidates and one clean elimination can open things up.
The logic
Every row and every column needs each digit 1–9 exactly once. If a digit's only candidates in a row are all inside one box, one of those cells has to be the digit — there's nowhere else on the row it can land. But a box only holds each digit once, so once the row uses up that digit inside the box, no other cell in the same box can have it. That's why every candidate inside the box, off the source row, can be crossed off. The same reasoning with a column swapped in gives the column version.