"ながら" is a conjunctive particle and it means "while". It is used when you do two things simultaneously. "ながらスマホ" is used when you do something while on the phone. (”歩きスマホ” means "a smartphone zombie" and it is used when you are walking while on the phone.)
Don't talk with your mouth full!
食べながら、喋らないで！
食べながら、喋らないで！
Ken is walking with Leo while looking at his phone.
- Leo : I made Sara mad yesterday. I was late for our date. Hey, are you listening?
昨日サラを怒らせちゃった。デートに遅れちゃった。ねぇ、聞いてる？ - Ken : Yes. It's about your girlfriend who easily loses her temper, isn't it?
あぁ。すぐ怒る彼女の話だろ？ - Leo : Yes. Watch out! (Suddenly, a stranger on the bicycle bumped into Ken. He dropped his cell phone.) It’s dangerous to text while walking!
うん。気を付けて！歩きスマホは(or歩きながらスマホを使うのは)、危ないよ！
Meg and Amy are gossiping.
- Meg : Do you know that Ken has cheated on his girlfriend?
ケンが浮気していたって、知っている？ - Amy : You don't say. He has gone out with Kumi for more than a year. In the mean time, he has dated Miki as well.
そうらしいね。一年以上もクミと付き合っていながら、ミキともデートしていたんでしょ。 - Meg : Honestly, he didn't strike me as the cheating type. I've officially lost faith in men.
正直(に)言って、ケンが浮気するようなタイプだと思わなかった。男の人が信用できなくなったよ。