To save up is a phrasal verb which means that you are deliberately keeping money aside so that you can buy something in the future. For example, I’m saving up at the moment so I can afford to go on a thrill-seeking adventure holiday to Sri Lanka and India next year. Unfortunately, at the moment, my piggy bank is completely, and utterly empty! Holy smokes, I need to cut down on buying bottles of wine, bars of chocolate and stupid saucepans! Somebody save me from myself!