Extroversion is a term that is used to describe a person's personality. It is one end of a continuum with the poles being extroversion and introversion. Extroversion is the personality trait of being outgoing.
People who are extroverted tend to be more interested in seeking stimuli from outside themselves than in keeping to themselves. These people would rather be with other people than alone. They tend to have a large number of friends.
Extroverts tend to be the sorts of people who work well in groups or who are seen as good leaders. They are able to do these things because they tend to relate well to other people.
Extraversion is a personality theory. Extraversion comes from "extravert" meaning a person who is outgoing, assertive, talkative, and has lots of energy. This person likes person to person interaction better than being alone or with a single person. An extravert would be considered an social person who seems happier when with other people.
The opposite of extravert is an introvert. This person would rather be alone or with a single person. They are quieter, less outspoken than an extravert, reflect on events and interactions, and they like to do things that involve calming activities instead of chaos.
Extravert can also be spelled extrovert.