Your casino account at any online casino is based on your log in name and password. Where you log in, there you can play. This means that you can play on your mobile phone, on your tablet and on your desktop or laptop, anywhere you want. But keep it cool ofcourse, don't be an addict!
Do you have more than one player in your house, under the same IP-adress, playing at the same casino? You should inform the casino. This is necessary to prevent the casino from thinking one person is using more accounts. A person is allowed to register for one account only.