The shell keeps a history of the commands that you type, that's what the history command gives you. There is no automatic history of the output from the commands that you run in the terminal. Once you close the terminal, the output is lost unless you saved it somewhere.

You can save a complete transcript of a terminal session by running the script command. If you run the command script, you get a new shell prompt; all the commands that you type from that point, as well as their output, are entered in the log. The log file is closed when you exit the script subsession (which returns you to the parent shell — entering exit or pressing Ctrl+D a second time exits the parent shell).

The default history file name is typescript (in the current directory). If there is already a file by that name, it is overwritten. You can specify a different file name by passing it as an argument to script, e.g. script hello.txt.

If you want to keep the history after closing a terminal, but don't mind losing the history when you switch off your computer, you can run screen or tmux.