I have been reading some code and come across
UNIQUE KEY User_name (User_name,Email)
UNIQUE KEY (User_name,Email)
This is known as a together unique index. When both fields are considered together their values cannot be repeated but individual fields may repeat.
For example there may be several entries in the username column called Tim, and there maybe several entires in the email field named email@example.com however there can be only one
If you want usernames to be unique (which is usually the case) you need to make that column unique on it's own (you can also make it the primary key).