It exists to reward early risk. An investor who backs you before there is much to see does not want their money converting at whatever price a later, more competitive round sets — that would mean taking the earliest risk for the latest price. The cap fixes a ceiling: convert at the round valuation or the cap, whichever gives the investor more shares.
For founders, the cap is usually the most consequential number in an early agreement, more than the amount raised. A low cap on a large early cheque can hand over a surprising share of the company when the priced round finally lands, and by then the terms are set. Caps also anchor expectations — the cap you agree today becomes the number the next investor argues from. Model conversion at several plausible round valuations before you sign, not after.
A concrete example: an investor puts $250,000 into a SAFE with a $5,000,000 cap. Your priced round comes in at a $15,000,000 pre-money valuation. Without the cap they would own about 1.7%. With it, their money converts as though the company were worth $5,000,000 — about 5% — roughly triple. The company did well, the early investor did very well, and the extra dilution came out of the founders' side of the table.