The Library contains information about all of your files. It doesn't contain the files themselves.
MC will backup the Library automatically on a regular basis, approximately every two days. The location of the Library backup file is determined by the setting in Tools > Options > File Location > Program Files > Library Backups.
You can back up your library manually if you need to, for example before you make significant changes to the library. Go to File > Library > Back Up Library. You can choose the location at this point. Note: this creates a backup of the currently loaded library. To back up all your libraries, open each one and repeat the process.
Also, remember that the backup will save the Library and all of your settings