The meaning is very close between celui-ci and celui-là. In theory, the first one is for things closer than the second one but this nuance is not always respected.

The third one has a different meaning.

They are close to the English: this one (celui-ci) , that one (celui-là) and this (ceci).

You are missing cela / ça for the English that.

Note that celui is masculine singular and must agree with what it refers to, e.g.:

celui-ci – celle-ci – ceux-ci – celles-ci

On the other hand, ceci and cela are invariable.