If cookies store an unique ID to track the user on server-side and the content of this cookies is transmitted to the web site owner, how can I monitor / know what type of information are they collecting ? I have EditThisCookie installed but other than the cookie flags and some random string number (is it the unique ID?) I cannot find really useful / human readable information.
how can I monitor / know what type of information are they collecting
Not at all. Since the information that is actually associated to you is stored server-side, you simply have no way of knowing.
The only thing you see is this cookie, which is really nothing but an ID to know that you are you.
So, there's no human-readable information in the cookie, because it typically only stores some session ID.
You can, from the existence of a cookie, however, infer that the server is capable of tracking which sites on that server you've accessed. This gets a lot more involved as soon as there's, for example, advertisement or content-delivery networks involved. Whilst you see multiple, different cookies that belong to different domains/servers, behind the scenes, these servers will be collaborating to "piece together" a more comprehensive picture of your e.g. surfing behaviour.
Facebook is a prime example. There's many sites that embed some Facebook widgets on their pages. Now, Facebook knows what site their widget is embedded in, and can track you, because you've got a facebook cookie (at the very least from the moment you've logged in) and are connecting to Facebook's servers to get the widget's content. Now, Facebook gets a history of all pages with embedded facebook widgets you're visiting.