Presidential proposal and congressional appropriation
The US budget process begins when the President proposes a budget to Congress, laying out spending priorities and revenue projections for the fiscal year. Congress then spends months debating, amending, and passing appropriations bills that specify how much each agency receives. This is the constitutional balance: the executive proposes, the legislature disposes. In practice, Congress often ignores the presidential proposal and writes its own budget.
Authorization bills specify what agencies can do (e.g., they authorize the Department of Defense to spend up to $850 billion); appropriation bills specify how much money they actually receive. Without an appropriation, agencies cannot spend money even if authorized. This distinction allows Congress to constrain an agency both by what it authorizes and by how much it funds.
From obligation to outlay
Federal spending involves a multi-step process. Congress appropriates funds, making them available. Agencies then obligate the money by entering contracts or commitments. Finally, agencies disburse (outlays) the cash. A large military procurement might be appropriated in year one, obligated in years two and three as contracts are signed, and spent (outlaid) across years three through ten as goods are delivered. This means annual appropriations and annual outlays differ significantly.
This complexity allows Congress to control yearly spending (by appropriating less than obligated) and allows the President to slow or accelerate outlays through administrative action. It also creates the persistent federal debt: deficit spending means government borrows to make up the difference between revenues and outlays.