I'm currently reading Understanding Distributed Systems. The author starts with few intro chapters and one of them touches security and cryptography. It briefly discusses ECC and gives very good reference to learn more.

I won't be able to describe it better than Cloudflare's blog does, so here is a quick and inaccurate summary. ECC stands for Elliptic Curve Cryptography. The idea of the cryptographic systems is to find so-called Trap Door Function. Trap Door Function is a function which is easy to do but very hard to undo. Most cryptography is based on that idea. RSA uses this as well and the "undo" function in RSA is called factoring.

In ECC, we have an equation. When we create a graph with it, then selecting two points on the graph we can point to the third point (by drawing a line through the two selected points). When we arrive to the third point we can either go straight up or straight down. Then we repeat such operation few times, and it becomes very hard to undo it.

This is very inaccurate description of ECC (this is not easy topic). The important facts are that ECC is a lot faster than RSA. This means that for the same number of bits, ECC is a lot stronger than RSA.

For more accurate description go here.