*I understand that there are similar questions on this site and on the web, but I've failed to find any that give a satisfactorily plain enough answer for me to understand, given my background, and therefore ask this question separately.
I understand the very primitive basics of category theory, as well as have a vague notion of some higher order (although admittedly not that high) ideas. However, I fail to understand what exactly the notion of infinity category theory is, what an infinity category even is, or how higher order categories relate to lower ones (if that's even the right language). Any help in understanding these ideas is greatly appreciated. In answering, please feel free to excuse some formality and speak with a degree of inexactness, as you see fit. I give more detail to my background and confusions below.
I get that there's some connection to homotopy theory, but I'm confused in that this always seems to be presented as an example rather than a foundation, despite me finding no other explanation for where infinity category theory comes from (I know that the foundations of infinity category theory is the subject of ongoing research; so maybe my inability to find a straightforward answer is because there is none?). I understand the idea of the homotopical interpretation of dependent type theory - is this the accepted foundation of infinity category theory? If so, then how does infinity category theory follow from it?
I also understand that infinity category theory has to do with defining equivalence (or just isomorphism? or something else entirely?) between some things (I'm not sure exactly what things) in terms of equivalences in the n+1-dimensional category, which in turn are defined in terms of that of the n+2-dimensional category, and so on. But what exactly is a "dimension" in the categorical sense (or at least in this context)?
As you can probably tell, my confusions and gaps in knowledge are rather scattered, but I feel as though I'm right on the edge of being able to understand. However, I also understand that I may simply lack the necessary understanding of more basic ideas in order to grasp the essence of infinity category theory, no matter how plainly it's spelled out for me. If you feel that that is indeed the case, then I would greatly appreciate references that I may use to try and fill in the holes that I've displayed above.
All comments and answers are appreciated, and all edits are welcome, as I'm aware that some of my language here may just be plain wrong or inaccurate. Thank you for your time!
**Per @hardmath's comment, I'd like to clarify that most of the reading I've done where the ideas I reference come from is Emily Riehl, in order to give authorial context. Other than her, my reading has been rather informal and scattered, which may give context to my confusions.