What is the difference between "local" and "roaming" folders?

Local stays with the user on that specific computer.

If you are on a domain, a "roaming" profile will be uploaded before you logoff. When you log onto another computer with roaming folders, all of your files in the roaming folder will be at the new computer too.

These folders were introduced in Vista with a view to making management of user profiles easier.

From this discussion:

Windows uses the Local and LocalLow folders for application data that does not roam with the user. Usually this data is either machine specific or too large to roam. The AppData\Local folder in Windows Vista is the same as the Documents and Settings\username\Local Settings\Application Data folder in Windows XP.

Windows uses the Roaming folder for application specific data, such as custom dictionaries, which are machine independent and should roam with the user profile. The AppData\Roaming folder in Windows Vista is the same as the Documents and Settings\username\Application Data folder in Windows XP.

In certain network settings, profiles roam with the user regardless of what computer they are on. That application data ultimately ends up in the "roaming" folder.

Some data is too large to roam, and ends up in the Local and LocalLow folders.