Open Settings → Accessibility → Display & Text Size → Color Filters , then turn Color Filters off. That usually restores the normal colors on an iPhone.

If it still looks black and white

  • Check Accessibility Shortcut in Accessibility, because grayscale may be tied to a shortcut and get turned back on accidentally.
  • Look in Accessibility → Zoom → Zoom Filter and set it to None if the display is still washed out.
  • If needed, restart the iPhone and make sure iOS is up to date.

Quick path

  1. Open Settings.
  2. Tap Accessibility.
  3. Tap Display & Text Size.
  4. Tap Color Filters.
  5. Switch Color Filters off.

TL;DR

Your iPhone is probably in grayscale under Color Filters. Turn that setting off and the colors should come back.