an email address

Matches an email address. It is anchored at both ends, so the whole string has to match. There are no capture groups.

Pattern

/^[^\s@]+@[^\s@.]+(?:\.[^\s@.]+)+$/

Try it yourself

Type any text and the parts this expression catches are highlighted. It runs in your browser and is never sent anywhere.

a@b.com

1 match

With ^ and $ around it, the whole string must match; without them the match can sit anywhere. Always anchor an expression you use for validation.
Round brackets ( ) capture what they wrap. When you only need grouping, write (?: ) so the numbering of later groups does not shift.
Every expression here is checked against its examples. Even so, "looks like an email" and "is a real inbox" remain different questions.
Nested open-ended repeats such as (a+)+ can blow up on certain inputs. Look for that shape before pasting someone else’s expression into your code.

Q. What is the regex for an email address?

^[^\s@]+@[^\s@.]+(?:\.[^\s@.]+)+$.

Q. Which strings match?

Text like a@b.com matches; text like a@b does not.

Q. Does the whole string have to match?

Yes. It is wrapped in ^ and $, so nothing but a full match passes.

Q. How do I use what it caught?

There are no capture groups, so only the whole match (match[0]) comes back. Wrap the part you need in brackets to capture it.