Refers to ones neighborhood.
Refers to a person whose experiences are limited to their local evironment. An individual who has a lot of attitude (not in a bad way); They haven't experience much of the world past their block.
It can also refer to someone who although they are worldly they maintain a down to earth quality.
- Yo I just ran into one of my homies I had not seen in a long time, he used to live around the way but he moved.
-You know she don't get out much, she's a round the way girl.
- She blew up, but she's still like a round the way girl