Hello,
Thank you for contacting us about exporting a Website. You can download a backup of your website files (it includes all of the website and email files from your user's home directory), or your Databases individually.
You can also perform a complete backup, which includes both files/databases.
Another option, is to download your files via FTP.
We also recommend performing these backups regularly, and before any major changes/maintenance.
Once you have the files/databases, you can upload/import them to your new host (they should be able to assist you with this like InMotion).
Let us know if you have any further questions.
Thank you,
John-Paul