The main source of errors in DFT calculations stems from the xc-functional, which isn’t known exactly. So what remains to obtain better results is to improve the xc-functional. However, this is a very complex expression which is likely impossible to guess. However, we can start by making very rough approximations, as LDA does, which is the first rung. As this gives good results, we can add another layer of complexity which is the second rung.
Each rung is an added layer of complexity, which if it gives better results than the previous one, gets us one step closer to the fifth and last rung which takes everything into account, and as such being the highest in complexity.