How it works
Find a digit with exactly two candidate cells in one row and exactly two in one column, where one cell from the row and one from the column sit in the same 3×3 box. Those two can't both be the digit — a box only holds it once — so whichever one misses out leaves its own line with nowhere else for the digit but that line's other cell. Either way, one of the row's or column's 'other' cells always ends up holding it, so any cell that sees both of those other cells loses the digit.
Try it
Look at Row 5, Column 7, Row 7, Column 7, Row 9, Column 3, and Row 9, Column 8 — a row and a column where 5 has only two candidates each, with one cell from the row and one from the column sharing a box. Let's pencil them in, then see why 5 can't survive at cells that see both of the two that *don't* share it.