Elliptic curves are special types of curves defined by cubic equations in two variables. They have a unique shape resembling a loop or an oval, and they are often used in mathematics and cryptography. The points on these curves can be added together using a specific set of rules, which makes them useful for creating secure communication systems. In the world of cryptography, elliptic curves provide a way to create strong encryption methods. They allow for smaller keys compared to traditional methods, making them faster and more efficient. This is why elliptic curves are popular in modern security protocols, such as those used in SSL/TLS for secure internet connections.