Rules and terminology
The puzzle is most frequently a 9x9 grid, made up of 3x3 subgrids called "regions" (other terms include "boxes", "blocks", and the like when referring to the standard variation; even "quadrants" is sometimes used, despite this being an inaccurate term for a 9x9 grid).
Some cells already contain numbers, known as "givens" (or sometimes as "clues").
The goal is to fill in the empty cells, one number in each, so that each column, row, and region contains the numbers 1-9 exactly once. Each number in the solution therefore occurs only once in each of three "directions" or "scopes", hence the "single numbers" implied by the puzzle's name.