Cool statement about vector spaces

I found this cool quote that for now still blows my mind and seems cool although I am sure at a later point I will have a better grasp on things.

"A vector space that does not have a finite basis is called infinite dimensional. This is not an exotic property: many of the most important vector spaces, particularly spaces where the "vectors" are functions are infinite dimensional"

The parts that blew my mind were infinite dimensional not being an exotic property and the concept of functions as vectors. I am sure it will make more sense later.