SSH gives you a command line on the server. It is enormously useful for anyone comfortable with it, and it is not enabled by default.
Asking for it
Open a support ticket. Tell us what you intend to use it for – running WP-CLI, importing a large database, managing files in bulk. We are not being difficult; knowing the purpose lets us make sure it will actually do what you need.
Connecting
Use a key rather than a password. Generate a key pair on your own machine, keep the private half safe, and send us the public half. Key authentication is both more secure and more convenient.
What you can do with it
- Move, copy and search large numbers of files far faster than through a browser
- Import and export databases without the size limits phpMyAdmin imposes
- Run WP-CLI, including a safe search-and-replace that handles serialised data correctly
- Read logs directly
What you cannot do
You are confined to your own account. You have no root access, cannot see other accounts, and cannot change server configuration – that is what makes shared hosting safe for everybody.
A word of caution
There is no undo at a command line. A mistyped delete removes files immediately with no recycle bin. Take a backup before anything substantial, and be especially careful with recursive commands.