Real computers have only a finite number of states, so what is the relevance of Turing machines to real computers? Real computers have limited memory and only a finite number of states.
So they are essentially finite automata.
Why do theoretical computer scientists use the Turing machines 
(and other equivalent models) for studying computers?
What is the point of studying these much stronger models with respect to real computers?
Why is the finite automata model not enough?
To complete the other answers: I think that Turing Machine are a better abstraction of what computers do than finite automata.
Indeed, the main difference between the two models is that with finite automata, we expect to treat data that is bigger than the state space, and Turing Machine are a model for the other way around (state space >> data) by making the state space infinite. This infinity can be perceived as an abstraction of "very big in front of the size of the data". When writing a computer program, you try to save space for efficiency, but you generally assume that you won't be limited by the total amount of space on the computer. That is part of the reason why Turing Machines are a better abstraction of computers than finite automata.