A bilateral contract is one where there is a promise for a promise. Sales contracts and listings are examples of bilateral contracts. In a listing contract, the seller promises to pay if the agent promises to procure a purchaser.
A unilateral contract is a one-sided agreement—that is, only one party makes a promise to perform. A lease option is a unilateral contract until the option is exercised. Another example of a unilateral contract is a lost dog sign—if you find the dog, you get paid, but you are not promising to go and look for the dog.