In legal terms, a unilateral contract refers to a contract between two parties where only one of the parties agrees to having obligations. This type of contract, despite the risky-sounding nature of it, is actually quite popular and commonly utilized for various purposes. The most common use for unilateral contracts is to offer a reward for some activity - for example, a person having lost their property may put up an announcement that they're offering a monetary reward for the location of said property. In this case, only the person providing the reward has an obligation (paying it out), while the other party has no obligation to find the property and return it - but will benefit from the contract if they chose to do so.
Unilateral contracts can be far more complicated than that, however - for example, in the above scenario, the party offering the reward could state further conditions for being eligible for a reward, such as finding the property in a given amount of time or delivering it in a good condition. In this case, even though this technically sets some obligations for the other party, they're still not obliged to engage in the contract at all, and it's thus still considered a unilateral contract.
Unilateral contracts are rarely used outside of this sense, as they involve a great deal of risk for one of the parties involved. In some cases, a party who wishes to engage in a unilateral contract must state their intents to do so before fulfilling the requirements of the contract.