Stashed on a server
A roaming profile in this context is one stored on a server. Each time your user logs in to a PC he has never used before, a copy of the profile is installed on it. In reverse, all changes to the profile are replicated to the server copy so they later reflect on other PCs as soon as the user logs in.
Local profiles are just that: they only exist on one client PC and are not replicated to other PCs even if the same user is able to log on there (so you get the default nearly empty desktop)
A roaming profile is normally defined by IT as you need to be able to set rights on the server and to change the domain account.
