Here's the mechanics. You invest $25,000 on a SAFE with a 20% discount. When the company later raises a priced round at $1.00 per share, your SAFE converts at $0.80 — so your $25,000 buys 31,250 shares where a new investor's $25,000 buys 25,000. The discount is the early-bird price: you took the risk before there was a priced round, and the discount is how that risk gets paid for at conversion.
Most SAFEs and notes carry both a discount and a valuation cap, and you convert at whichever gives the lower price — they don't stack. That means the discount does the work in modest rounds: if the round prices below the cap, the 20% off is what sets your price. If the company takes off and the round prices well above the cap, the cap sets your price and the discount is irrelevant. A discount alone, with no cap, is a weak deal in a breakout — 20% off a huge valuation is still a huge valuation — which is why caps became the standard companion. When you see a discount quoted on a deal, the two questions to ask are whether there's also a cap, and what the discount implies about how founders expect the next round to price.