Spiderman s eyes move in Captain America: Civil War?

A similar effect was used on Deadpool's eyes. It adds a layer of emotion to his suit. Or maybe it was used to help Peter focus/see better since his senses were "dialed to 11." If it's not your cup of tea, don't fret, his suit will surely change down road (remember Captain America's suit in the first Avengers movie? lol).

Lens focusing.

If you remember the scene in Parker's bedroom, he tells Stark that he wears goggles because his vision has been enhanced. Sometimes its hard for him to operate with his new eyesight. So presumably Stark designed vari-focusing goggles into the new suit to allow Spiderman to utilize the range of his eyesights abilities.

It was a new suit designed by Tony Stark, it was mentioned briefly in the movie. Why? It seems like it's just Stark showing off

It kind of works like a camera lense. When he does something that triggers movement in a certian area, the eyes move like a camera

To make him look like he's focusing in some sort of anger