So, in all of the animation type threads people always say things like, "beginner" and "intermediate". and they don't seem to use them in a general sense; is there a ranking system?
Please tell me what it means, and thank you.

Well...It is like a rank. It means how good his/her animating skill is. For example: I'm a novice which means I'm between beginner (which means noob or new in animating) and adept (slightly good).

Here, I'll even give ya a short list of 'ranks/skills'

Beginner - New at animating/ Isn't good yet.
Novice - Kinda good at animating
Adept - Slightly Good
Intermediate - Animating Skill is normal (There easing/fluidiness is smooth and doesn't have much mistakes or need improvements in animating)
Expert - Very good ( Rare to have mistakes or need improvements in animating.)
Terkoiz Level - As the name says, His skills is like Terkoiz's

(Not sure if this is accurate...)

okay, thanks! but my main question is more like this; how do you know what somebody's (or yours) rank is?

There's no such thing as rank. It depends on your animating experiences and skill. Like you're already a pro after joining the animating team and then suddenly you became a noob.
Terkoiz is a highly trained and experienced animator, so does, Hyun, Endo, Jomm, and yeah those kinds of animators.
I myself am just a normally trained animator. So yeah.

This has been mentioned a lot of times that there's no Animation Rank,Skill nor Level though they saying sometimes at animators as noob but it doesn't make sense.

Yeah okay . Thanks everyone. Its just that everyone always seemed to say, like in a collab or whatnot, "skill level must be intermediate" or something. I was just wondering what it means.

When people says intermediate, it basically means that you know and use flash in a proper manner and that you domain the principal "rules" when animating, such as smoothness, easing, acceleration and stuff. But there is no thing as a rank system or something like that

Fuck ranks. There are problems with your animation and you should work on fixing them, or your animation is perfect and you should work on something harder. Those are the only options. Ranks are for people who are insecure with other people animating differently to them.