back and forth

adverb

Going from one place or position to another and back again.
“The back and forth movement of the tide causes erosion of the coastline.”

From one place to another and back again.
“One frigid November evening, the mood was buoyant as two dozen mostly older Chinatown residents poured into the center. One by one, they tossed their parkas on chairs and took turns at the karaoke machine. Soon, the room was alive with people dancing and singing under a haze of blue strobe lights. A projector flashed images of the Chinese countryside and women dancing in embroidered, silk costumes. Nearby, younger people darted back and forth at Ping-Pong tables.”

The movement (of someone or something) forward followed by a return to the same position. May refer to a concept such as an emotional state or a relationship as well as a physical thing.
“Roll the ball to your child, who then rolls it back to you. After a few back-and-forths, roll the ball to a nearby corner of the room or other hiding place.”
Negotiations or discussions (not necessarily fruitful) between two or more parties; a dialog.
“There's some back and forth between Simpson and his CIA counterparts and, in essence, the CIA says that you must ship all of the quantities requested.”
“It was months and months of back and forth, ah-ah, ah-ah You're still all over me like a wine-stained dress I can't wear anymore”