ARRAYFORMULA lets a formula work on whole ranges at once. =ARRAYFORMULA(C2:C15*D2:D15) multiplies row by row and spills 14 answers down the column from one cell. Nothing to fill down, and no copy of the formula in every row to fall out of step.
Typing a formula and pressing Ctrl+Shift+Enter (Cmd+Shift+Enter on a Mac) wraps it in ARRAYFORMULA for you. Without it, =C2:C15*D2:D15 in E2 just returns one value, the one for its own row.
Pair it with an open-ended range, C2:C, and new rows are calculated as soon as they're typed. The catch: empty rows give 0 all the way to the bottom of the sheet. Wrap the math in IF to keep them blank: IF(A2:A="", "", C2:C*D2:D).
Most functions that take one value, like IF, VLOOKUP and LEFT, work row by row inside ARRAYFORMULA. Functions that sum up, like SUM and AVERAGE, still return one total, so ARRAYFORMULA(SUM(C2:C15*D2:D15)) totals the products without a helper column.