You want to leave a process running (often on a remote computer), and you want the process to keep running even if you close the terminal session (often running on a local computer).
First start a screen session using
user@remote ~$ screen -S [name]
[name] is any meaningful identifier for you to remember.
Now you can start your processes, and close the terminal window if you want to.
Later, to recover your session use
user@remote ~$ screen -d -r [name]
so that you can get your session back and monitor the processes that you left running.
If you forget the name of your screen session, you can also always type
user@remote ~$ screen -ls
to see a list of all the currently active “screens”.