Sometimes a formula should follow the row in one direction and the column in the other. A pricing grid is a good example: each cell multiplies a value from the left edge by a value from the top edge.
$A3 locks the column: copied right it stays on A, copied down it moves to A4, A5...B$2 locks the row: copied down it stays on row 2, copied right it moves to C2, D2...
So =$A3*B$2 in B3, filled across and down, multiplies "the value at the left of my row" by "the value at the top of my column" in every cell.
The rule of thumb: put $ in front of the part that must not change as you copy. Press F4 two or three times to reach the mixed forms (B$2, then $B2).