The term intertemporal is used to describe any relationship between past, present and future events or conditions.
In its general form, the intertemporal budget constraint says that the present value of current and future cash outflows cannot exceed the present value of currently available funds and future cash inflows.
In most applications, the entire budget would be used up, because any unspent funds would represent unobtained potential utility.
In an intertemporal consumption model, the sum of utilities from expenditures made at various times in the future, these utilities discounted back to the present at the consumer's rate of time preference, would be maximized with respect to the amounts xt consumed in each period, subject to an intertemporal budget constraint.
Since investment returns in each period generally would not be known in advance, the constraint effectively imposes a limit on the amount that can be invested in the final period—namely, whatever the wealth accumulated as of the end of the next-to-last period is.