SQL Express uses 2 files per database one with the extension MDF and another with the extension LDF. You'll need both for your database to work. I have never tried to copy the files from one machine to another. I normally backup the files from one machine and restore to another machine and overwrite a db that already exists.
That said it looks like you might be able to copy the files from machine A to machine B and then on machine B, with SQL manager Connect to the SQL Server (localhost or whatever) Right click Databases folder Left click Attach, Add Point to the MDF you want to start using and you should be good to go.