The illusion of self is a big deal in Buddhism and it can be confusing and daunting at first, but the concept behind it is really not that difficult to grasp. (Putting it into practice is a different challenge!)
One analogy I like to use is that of an automobile. The individual parts - the engine, the wheels, the chassis, the steering wheel, the gears etc - are all necessary, but individually, none of them are the car themselves. No one would look at a seat and say "that's a nice car!" Yet, we do just that in our daily lives.
We experience anxiety and fear and say "that's ME!". We go through several bodily experiences as "I, me, mine". (Which is NOT the same as saying this body is not you. Think of the car analogy. The tears are happening to you, but the tears are NOT YOU.)
Therefore, in all Buddhist traditions, we are taught to view all experiences as fundamentally lacking any self. This body, this experience, this thought, this taste/smell/touch, nothing has the self. Those are all beautiful but empty experiences.
Hope this answered your "illusion of self" question at least partly.
That's not the illusion I was talking about though. It's one thing to read about that, but it's quite another to directly experience this. Like @kordless said, this is a repeatable process where you can see this for yourself. (And there's a great book written by a neuroscientist who also practices mindful meditation, and wrote about these two perspectives).
This is also not limited to the Buddhist tradition, though the sutrayana Buddhist teaches this as the primary thing and speaks the loudest about it. (There are ... realms, let's just say, beyond no-self and emptiness).