According to the "Oxford Dictionary of Economics," an intertemporal budget constraint is "the requirement that the total spending of an individual, firm, or government must be within the funds available to it over some long period."
For an individual ,an intertemporal budget constraint is straightforward. An individual's budget is constrained by the amount they earn or expect to earn in their lifetime plus the value of any assets they possess. If you sold all of your assets and added that money to the amount you are likely to make in your lifetime that would be your spending limit or intertemporal budget constraint.
Because governments, institutions and corporations are theoretically immortal, the equation for a intertemporal budget constraint changes significantly. To set a constraint, the government, corporation or some third party must set an end date. So, as an example, a government might set 2025 as the end date for budgeting and establish its intertemporal budget constraint as the money plus assets they are likely to have by that date.
Complications can arise with intertemporal budget constraints because of economic uncertainty. This is true for individuals as well as governments and corporations. Because no one can adequately predict economic factors such as unemployment and interest rates, especially over the long term, and because no one can predict when an unforeseen crisis may arise, predicting actual income over extended periods is difficult.