as an adjective, 'own' is used to emphasize that something belongs to or is connected with a particular person or thing.
I made this cake with my own hands.
She has her own apartment in the city.
They want to start their own business.
as a pronoun, 'own' is less common and is used to emphasize the fact that someone does something for themselves without assistance.
She baked the cake on her own (meaning she baked the cake by herself).
I want to do it on my own.
They went on vacation on their own.
when used as a pronoun, 'own' is often paired with 'on' to mean 'by oneself' or 'without assistance.' As a pronoun 'own' is always placed at the end of the sentence.
as a verb, 'own' means to possess, have, or hold as one's own.
She owns three cars and a house.
He owned up to his mistakes.
Do you own this book?
'Own up to' is a phrasal verb meaning to admit or confess something.