iCloud Mail and Notes requires an iCloud email account with the @me.com address. If you do not have an @me email address associated with your Apple ID (for example if you use your @hotmail.com or @gmail.com email when you setup an Apple ID), you will be prompted to create one the first time you enable iCloud Mail or iCloud Notes.
The following screenshot shows the prompt to create a free @me.com email account on an iPhone when you turn on Notes under Settings>iCloud. For OS X, it is under System Preferences>iCloud.
The @me.com email address you created can not be changed thus you might want to choose the name carefully. Once the @me.com email address is created, iCloud will link this new email address to your Apple ID to enable iCloud Mail and Notes.
When you visit appleid.apple.com to manage your Apple ID, you will find your new @me.com address under the entries for “Alternate Email Address”:
Technically iCloud Notes is using the notes feature available within an email account. This notes-within-email feature has been around for a while. For example the notes under GMail is using the same email mechanism underneath as in iCloud Notes. Apple chooses to reuse this standard email feature rather than creating a separate app for iCloud Notes. Apple probably requires a @me.com account as it enables them full control in order for the interface between iCloud and email note to work.
You probably question the need for yet another email account If your main email is not the @me.com account. Fret not, as you can simply treat the @me.com as an enabler for iCloud Notes feature and ignore its existence. Adding this new @me.com also does not affect how you use your Apple ID as your primary email account for Apple ID remains unchanged.