A SAFE is a contract created by Y Combinator in 2013 to standardize early-stage investing. Unlike a convertible note, a SAFE is not debt: there's no interest, no maturity date, and no repayment if the company fails. It converts into equity at the next priced round, usually at a discount, a valuation cap, or both.
SAFEs come in pre-money and post-money flavors; the post-money SAFE introduced in 2018 is now standard at YC. SAFEs are popular because they close fast (a few hours of legal work) and avoid the complexity of negotiating a priced round at the earliest stage.