Here's a concrete example. You invest $50,000 in a convertible note with a 20% discount, an 8% interest rate, and a $5M valuation cap. Two years later the company raises a priced round at a $10M pre-money valuation. Your note has accrued about $8,000 in interest, so you're converting roughly $58,000. Because the round price is above your cap, you convert at the $5M cap rather than the $10M round price — effectively buying your shares at half the price the new investors pay.
The two features that don't exist in a SAFE are the ones to watch: interest and a maturity date. Interest increases the dollar amount that converts, and the maturity date is a hard deadline by which the note must either convert, be repaid, or be renegotiated. In the rare case a company never raises another round and the note matures, the investor is technically a creditor — though in practice early-stage startups rarely have the cash to repay, so notes usually get extended. Most seed deals have moved to SAFEs because they avoid this debt machinery, but you'll still see convertible notes, especially in bridge financings between rounds.