Definition

Let $(Y_{i})_{i\ge{1}}$ be a sequence of random variables, we say $(Y_{i})$ is exchangeable if every finite dimensional distribution of $(Y_{i})$ is the same as the corresponding finite dimensional distribution of $(Y_{\pi(i)})_{i\ge 1}$ where $(\pi(i))_{i\ge 1}$ is any permutation of $1,2,\dots$.

i.e. One can reorder the RVs in any way and it won’t change the distribution.