1 general:: Accumulate something for a particular purpose, as in Jan had been saving up her allowance for a new bicycle. [First half of 1800s]
American Heritage Idioms
2 general:: Phrase(s): save something up to save something; to accumulate something. • I’m saving up cans for recycling. • If you’d only save your money up, you could buy anything you want.
McGrawhill's American Idioms And Phrasal Verbs