"Putting your hair up" means styling your long hair in some way so that it's not just hanging down on its own. Some different hair stlyes that are considered "putting your hair up" include:
- putting it in a ponytail
- putting it in a bun
- braiding it
The opposite action from "putting your hair up" is "letting your hair down".
You can also "wear your hair up" or "wear it down".