Consider ab- in abbiegen as away. You "turn away", so to speak. That is, you turn away from the road, or plainly said: You leave the road.
The opposite is einbiegen where ein means onto and you turn onto the road.
The verb biegen, however, doesn't indicate the direction it just states that you turn or that something (e.g. a road) bends.
As this isn't really telling a lot, you normally describe the kind of turning with a prepositional phrase. A very common one is "um die Ecke".
Er biegt um die Ecke.
In respect to this very meaning, I don't consider biegen a common word in comparison to ein- and abbiegen.
Here are a few further examples taken from the Duden. The prepositional phrase is put in italics.
Der Weg biegt um den Berg.
Der Wagen ist eben in eine Toreinfahrt gebogen.
Sie bog rasch zur Seite. (=> Sie wich zur Seite aus.)
Note, "Langsam biegt ein Lastwagen um die Ecke ab." is correct, too. But it contains redundant information and, therefore, you won't hear it too often.