I'm reading up on the structure of SQL data, how the data is stored and whatnot, and I came across this site: SQL Server Data Structure One of the very first things it says is that a row can only reside on one Page, each Page can only contain 8kb of information, and thus due to this, the maximum size of a row is 8kb.

Makes sense, but what bothers me is that I can store more than 8kb of information in a row using nvarchar(max) and whatnot. I just created a 100kb .txt file and copy/pasted that into one field of one row in my database, and sure enough, it accepted it and it works.

So how can each page only be 8kb, and each row can only utilize one page, and yet still somehow manage to fit data much larger than 8kb?

Here: Understanding Pages and Extents
there is a Large Row Support paragraph that answers your question.

In short, large datatypes may be stored separate from the data page for the record, with the record only holding a pointer to the location of the actual blob.