An algorithm is a mechanical procedure that you can follow in order to achieve a result.
Algorithms are always formal, that is, symbolic.
The algorithm is just a set of rules for manipulating those symbols, based only on their shapes, not on what they mean. But the manipulation will give you a correct solution to some problem. You apply the formula to, say, measurements of barometric pressure and humidity, and you calculate tomorrow's temperature. Those are just words, symbols. But if you follow them and apply them to sugar, butter, etc., they will mechanically generate a cake.