Outgoing is an adjective that describes someone as friendly and sociable.
He socialises a lot, he is a very outgoing person.
Outgoing can also be used as an adjective to describe leaving a place, or leaving a job, having finished a period of time in it.
The outgoing president has left the country virtually bankrupt. (It doesn't mean the president was sociable, just that he is leaving.)
Going out (from to go out) is a phrasal verb that means to leave a room or building, especially in order to do something for entertainment purposes.
We're going out tonight. Do you want to come with us?