The conjugate gradient method aims to solve a system of linear equations, Ax=b, where A is symmetric, without calculation of the inverse of A. It only requires a very small amount of membory, hence is particularly suitable for large scale systems.
It is faster than other approach such as Gaussian elimination if A is well-conditioned. For example,
A=U*diag(s+max(s))*U'; % to make A symmetric, well-contioned
Conjugate gradient is about two to three times faster than A\b, which uses the Gaissian elimination.