Validating email addresses is now considered bad practice (stop validating email addresses with regex), especially with such expression as in your question. For example here's a more complete expression.
As for this expression let's break it in parts:
Beginning of the matched string
^
Matches at least one character from the list
[a-z0-9!#$%&'*+/=?^_`{|}~-]+
Non-capturing (see backreference) group which can be repeated 0..n times, that matches a .
and then at least one character from the list.
(?:\.[a-z0-9!#$%&'*+/=?^_`{|}~-]+)*
Just this character
@
Non-capturing group matching one character in this list [a-z0-9]
and then possibly more characters from the following lists. Matched string must start and end with [a-z0-9] and inside it can have [a-z0-9-].
(?:[a-z0-9](?:[a-z0-9-]*[a-z0-9])?\.)+
Non-capturing group that matches 2 uppercase letters or one of the words.
(?:[A-Z]{2}|com|org|net|gov|mil|biz|info|mobi|name|in|aero|jobs|museum)
End of the string.
$
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