There are various things that you can do, depending on the options in the rewire box. Often they open doors and the like, but also:
- Air Purifier fills the area with smoke that reduces visibility, allowing you to sneak past enemies. They also allow you to remove poison gasses from some areas so that you can get through them.
- Alarm and Speakers cause enemies to go and investigate - for the Alien this can be a very small window, as it goes there, looks about and often then comes straight back. Alarms work from further away but take a lot longer to reset and be used again.
- Lights turns lights on an off. Both can be useful as enemies will investigate the change of state.
Check the map on the right of the box, and RB and LB can switch rooms for many rewire boxes, as you can see exactly where the distraction will happen.
The distractions can be especially useful when the Alien is loitering where you need to go, which it seems to do all the time, and rewire boxes can buy you the time you need to get to the next objective. They're incredibly useful.