Question: How does algebra relate to this chess notation?

Why do they call this chess notation **algebraic**?

Answer: 
I think that Jonathan Garber is right. Much of algebra has to do with equation in an x y coordinate plane which is very similar to the way that algebraic notation denotes specific squares on the board. I have however not been able to find any specific source of the information.
Algebraic notation is quite old. It is based on a system created by Philipp Stamma (c.1705–55) *before* descriptive notation started to evolve. There is no indication that anyone with a mathematical background had anything to do with its development or spreading, so my best guess is that they called it "algebraic" simply because it uses coordinates. The funny thing is that there is nothing algebraic about coordinates. If anything, it should be called "geometric notation", but somehow "algebraic" sounds better; as if it is more accurate.

In brief, I strongly suspect that they **just** called it "algebraic".