How to fix hose bib?
You are looking at a sillcock. The piece you removed goes into a larger pipe and the actual valve is at the end of the pipe, inside the house. When you turn on the water, the valve at the end opens up and water flows through the pipe and out.
You should be able to remove and replace the entire assembly simply by turning the outside spigot counterclockwise and getting one the same size. You might be able to get replacement parts from a plumbing supply store.
The below picture illustrates a normal spigot and then a sillcock installation.