what is a MobileMe subscription

There is no such thing anymore, as MobileMe was discontinued and the service shut down back in late 2012.

Anyone who had a MobileMe subscription, with an @me.com (and possibly also an @mac.com) email address was able to move them to iCloud if they did so before the shutdown in 2012. Those older Apple email address from then on remain useable as aliases to one’s @icloud.com inbox -> iCloud: About your @icloud.com, @me.com, and @mac.com email addresses - Apple Support

The history is available at https://en.wikipedia.org/wiki/MobileMe

Where are you encountering MobileMe? That service was discontinued in 2012.