A dollar today is worth more than a dollar promised tomorrow, not because prices moved, but because the dollar today can be put to work in the meantime.
The time value of money holds that a given sum available now is worth more than the identical nominal sum available at some future date, because money in hand can be invested, lent, or otherwise deployed to earn a return during the intervening period. This is the load-bearing assumption behind nearly every standard valuation technique in finance: discounting (converting a future cash flow into its present-day equivalent using a discount rate) and net present value, NPV, (summing a stream of discounted future cash flows to judge whether an investment is worth undertaking) both depend on it.
Irving Fisher gave the concept its canonical formal treatment in The Theory of Interest (1930), arguing that the interest rate emerges from the interaction of two forces: time preference (people’s general impatience for consumption now over consumption later) and the investment opportunity principle (capital deployed today can be productive and grow, so waiting has a real cost). Later textbook treatments typically add two further factors: inflation (future money is expected to buy less, further eroding its value relative to money held now) and risk or uncertainty (a future payment might not arrive at all, so it is discounted for that possibility too). Together these give the standard justification for interest itself: the rate charged on a loan is framed as compensation to the lender for giving up the use of their money, and its earning potential, for the loan’s duration.
Once accepted, the time value of money supplies the logic for pricing bonds, valuing annuities, comparing investment projects, and setting actuarial and pension calculations, essentially any decision that compares cash flows occurring at different points in time.
Source: Fisher, I., The Theory of Interest, Macmillan, 1930.