ECC stands for Elliptic Curve Cryptography. Elliptic curves are a mathematical structure which allow to define cryptographic operations on them.
Elliptic Curve Cryptography is used in public-key cryptography, and is based on the algebraic structure of elliptic curves over finite fields: The security of ECC depends on the ability to compute a point multiplication, and the intractability of computing the multiplicand given the original and product points.
The benefits of ECC compared to other systems (such as RSA), is a smaller key size, which reduces requirements for storage and transmission. ECC is suitable for digital signatures, key-agreement, and pseudo-random generators, among other things. Due to it's limited computational requirements, ECC has been used on devices with limited computational power, such as RFID devices.