This formula is designed to be copied throughout the interior of the multiplication table without change. In other words, when the formula is copied to other cells in the table, the references will automatically update as needed to calculate the product of the corresponding row and column.
In $B5, the column is "locked" so that it won't change, and in C$4, the row is locked.
As the formula is copied, this is what the references look like for the first 5 rows and columns:
Mixed references are a common feature in well-designed worksheets. They are harder to set up, but make formulas much easier to enter. In addition, they are a key strategy for preventing errors since they allow the same formula to be copied to many locations without manual edits.