One of the 3x3 subgrids
Box 1 is the top left box, Box 2 is the top middle box, Box 3 is the top right box
Box 4 is the middle left box, Box 5 is the middle box, Box 6 is the middle right box,
Box 7 is the lower left box, Box 8 is the lower middle box, Box 9 is the lower right box
See Introduction for a visual
One of the nine possible digits of a cell.
The candidates of a cell are the cell's possible digits.
One of the 81 small squares on a 9x9 sudoku
By virtue of 9x9 sudoku, "Every row, column, or box must have the digits from 1 to 9".
Digit from 1 to 9
Solved or given digit
(theoretically possible for use in some obscure and contrived explanation) Digit from 0 to 9
Whatever's already provided at the beginning, before you start working on the sudoku. Especially a given digit.
Example: "The very easy sudoku in the Introduction has 80 givens!"
A row, column, or box.
A cell sees another cell if they're in the same group
A cell sees another digit if they're in the same group
A candidate sees another candidate if
They're in the same cell
They're the same digit, and they're in the same group
A cell is solved when you know what digit it has. (It only has 1 candidate left.)
A solved digit is the lone candidate of a solved cell.
All givens are solved digits.