How to understand the de-correlation property of DCT? What does de-correlation mean?
The term &quot;decorrelation&quot; generally accounts for processing that reduce autocorrelation within single, or cross-correlation within a group of  signals or  images. Doing that, it should preserve important features in the  data.

In other terms, images often contains simpler &quot;objects&quot; (in terms of  morphology: bumps, edges, textures) that are mixed, or distorted. Generally, unmixing them via decorrelation somehow simplify further processing.

Generally yes, unless you have uncorrelated noise in your images. A classical and simple model is an order-one Markov or autoregressive process. Basically a pixel somehow  depends (with a parameter $\rho$) on the past pixel, with uncertainty. If $\rho$ is close to $0$, you are already decorrelated. If $\rho$ is close to $1$ (typically $0.90-0.95$), the  data is quite correlated.


The DCT was meant for diagonalizing the  resulting autocovariance matrices with  Toeplitz structure, to give fast estimates of their eigenvectors. Transforming a fat autocovariance matrix into a thin, close to a diagonal, matrix is an instance of decorrelation.