It depends on the skin you’re using. To copy the album, from within jAlbum use Tools>Open directories>Output directory. In your OS copy the folder that is selected, it is called album’ by default.
If you are using a json based skin, like Tiger, the album needs to be viewed via a server. If you don’t have a local server you can use jAlbum’s. In that case you should copy the whole project, that is normally the folder enclosing the ‘album’ folder. Note, if using jAlbum as a server, place the projects in a folder called ‘My Albums’ and point jAlbum to that folder in Preferences >Projects>My albums.
Unless you have an extremely large projects you can just copy the single project or all projects (My Albums).
See
https://jalbum.net/help/en/JAlbum/Where_are_my_files
For information on what files go where and how to move projects to a different computer.