This is the 29th most frequent Finnish word.
hänen
"His" or "her" (gender-neutral possessive pronoun).
The word 'hänen' is a possessive pronoun indicating that the house is owned by 'him/her'.
Hänen talonsa on punainen.
His/her house is red.
The word 'hänen' specifies the person who was observed walking, used here as a pronoun to indicate the subject.
Näimme hänen kävelevän koiran kanssa.
We saw him/her walking with a dog.
In this sentence, 'hänen' is used to describe ownership or association with the described behavior.