It has a currency, a total for the whole mandate, and a limit per call, which is a ceiling on one call's worst case. A daily limit is optional; when it is set, spending resets at the start of each day. A budget also carries the conversion rates the gateway may use, and an agent priced in a currency the budget has no rate for is refused.
The check happens before anything runs, and it counts money that is only promised. The worst case of each call in flight is reserved, and admission compares the ceilings against what has settled plus everything reserved. So ten calls running at once cannot together overrun a total that none of them exceeds alone, and the reservation goes back when a call fails or costs less than its ceiling.
Example: a budget of 50.00 EUR in total, at most 3.50 EUR per call, and at most 5.00 EUR per day lets an agent run all week without a single call ever putting more than 3.50 EUR at risk.