Mari (possibly Jenkins, possibly something else) is the daughter of Megan, who is Wizard Howl's sister in Wales. Mari shows up only twice in Howl's Moving Castle: Once when Howl (along with Sophie Hatter) visits Wales to look into what a page of his nephew's homework is doing in the moving castle while an actual functioning magical spell is gone, and once when he sees a vision through one of the castle windows that lets him see a threatening scene in Wales that needs some intervention on his part.
Howl loves Mari, and she loves him with that uncritical reaction of a small child to a fond, attentive occasional visiting relative.
His relationship with Mari's brother Neil is more complicated, as it would be with any teenager, and his relationship with his sister Megan is still moreso. It's obvious why Howl left Wales and doesn't go back a whole lot.