Shears are handheld iron tools required for using the Tailoring skill. Like other common tools (Mining Axe, Blacksmith Hammer, etc.), the Shears will eventually break, at which point you can simply buy another one. They can be found at the General Store, Tailor Shop, or Tinker Shop.
Alternatively, anyone with Tinkering Level 3 can construct a pair of Shears with a single ingot. This is often done by aspiring tinkerers who are hoping to hone their skills.