What does merging equipment do?

Merging equipment will take it to the next grade level, and will usually unlock a new skill for the equipment. There are some more details on merging equipment here: https://www.appgamer.com/survivorio/equipment-guide

If you have two of the same items you can merge them to get it to the next level provided that they are on the same grade level. Totally worth it and just about the only way to get yellow or red equipment.