What does it mean when the constitutution says the president can recommend a budget to congress?

What happens is that the president's staff prepares a proposed budget and sends it to leadership in Congress. They then do what they want to do. Once the budget bill is passed, the President could veto it if he does not like it, but rarely does so for a variety of reasons. (By the way, the Constitution does not say that the president can recommend a budget .)