Using over as an adverb emphasizes a distance between two places but doesn't change the meaning of a sentence.
The use of over in this context makes a sentence somewhat informal or conversational in tone.
I'm flying over to London. = [more formal] I'm flying to London.
He followed her over to the table. = [more formal] He followed her to the table.
However, in some sentences, the over is necessary:
I'll be right over. = I'll be right there.