An elliptic curve is a type of smooth, continuous curve defined by a specific mathematical equation, typically in the form y^2 = x^3 + ax + b. These curves have unique properties that make them useful in various fields, particularly in number theory and cryptography. They are characterized by their shape, which resembles a loop or an oval. In cryptography, elliptic curves are used to create secure encryption methods, such as the Elliptic Curve Cryptography (ECC). ECC allows for smaller keys compared to traditional methods like RSA, while still providing a high level of security. This efficiency makes elliptic curves popular in securing communications and digital signatures.