This phrase describes a person doing something unexpected. For example:
She gave it to him for free, and then he turns around and sells it for a thousand dollars.
I saw her break it with my own eyes, and then she turned around and acted like she didn't know anything about it.
It's often used for unexpected bad actions, but it can also introduce surprising positive things as well:
He was shooting horribly until half time. Than in the second half, he turns around and scores 24 points.