Box/Line Reduction
When a digit within a block is confined to one row/column, it can be eliminated from that row/column in other blocks.
Box/Line Reduction exploits the intersection of blocks with rows/columns. When all candidates for a digit within a block align in a single row (or column), that digit must appear in that row within that block. Therefore, it can be eliminated from the same row in other blocks. This is a generalization of Pointing Pairs.
Two Directions
Pointing direction: candidates in a block confined to one row/column allow elimination in other blocks along that line. Claiming direction: candidates in a row/column confined to one block allow elimination from other rows/columns within that block. Both use the same logical principle.
Importance in Hard Puzzles
Box/Line Reduction is the first technique to try when Naked Singles and Hidden Singles cannot make progress in Hard puzzles. It reduces candidates rather than placing digits directly, indirectly creating conditions for single-type techniques to fire again.