From Tiny Life Wiki

Sometimes, objects will break, rendering them unusable. Tinies can repair objects, allowing them to level up their Repair skill.

The higher their Repair skill, the faster they can repair objects.

In-Game Description
"When something breaks down, and you don't have enough money to call a repairperson, you gotta get in there yourself! Take a spanner, a screwdriver and maybe some good old-fashioned tinkering experience, and get to work!"