“I saw her walking down the street, playing with her phone.”
You're telling a story about your sister who seems to check e-mail on her mobile phone too much. You've seen her use her phone in many situations, but yesterday you were surprised to see that she was using her phone even while she was walking. You tell your friend this about your sister.
I saw her walking down the street, playing with her phone.
You might think that you'd use "on the street" to describe a person who's walking. You do use "on" when someone is just standing:
I saw her standing on the street.
But when someone is walking or running, they do it "down" the street like in the example at top.
You can also use "up the street" when someone's moving away from you:
If you walk up the street a few blocks, you'll see a florist on your right.
In the example above, the speaker says "walking down the street, playing with her phone". This describes a person who is doing both of those actions at the same time. Also use this format with "sitting":
He was sitting at his desk, reading something on the computer screen.
This doesn't work for all actions, but when one of the actions is "walking", "running", "standing", or "sitting", you can use this type of sentence to talk about doing two things at once.
Children "play with" toys. When adults use something like it was a toy, you can say that they're "playing with" it. In the example at top, the speaker says that someone was "playing with" her phone. That makes it sound like she wasn't doing anything important with her phone and was playing with it like it was a toy.