drove over to

[WilliamTaft]

An example sentence using "over" in Collins COBUILD Advanced Learner’s Dictionary:

I got out the car and drove over to Dervaig.

What's the difference if I omit "over" in that sentence?

 

[teechar]

Look at the next entry (#11) in that link. In such sentences, "over" is used when the distance involved is not considered long.
Otherwise, there would be no difference in meaning if you omitted it.