Maahinen (pl. maahiset) is a creature which lives underground. This name includes a reference to the ground, maa, but another term used for them is hiidenväki "force/folk of Hiisi", and Hiisi probably here refers to the underworld. Apparently in Satakunta, there is a completely different kind of flying creatures called hiidenväki; we're not speaking of them here. Despite the name maahinen, hiidenväki have also been descibed to live in mountains and underwater. In Northern Finland, the terms vanha väki "old folk" and vanhaset "the old ones" have been used, and for Forest Finns, the term moanpitävät "keepers of the land".
By their appearance and way of living, maahiset resemble humans. They are not Christians, they dress and live in old-fashioned ways, they demand clean and honourable living, and they've been offered sacrifices of food and money. They are likely then those who were indeed buried underground: our ancestors. You need to ask a permission from them first before building a building, for if they don't like you, they cause illnesses and disasters. They seem to run in the same business, then, as the elves of Iceland.
In later folklore, maahiset developed features of household spirits, fairies and gnomes, who could be restricted with steel items. According to a Forest Finnish tale, there had been a maahinen Lady with huge amount of cattle, playing a horn while wearing a glorious golden crown. Indeed, according to Finns near Rear Bothnia and Torne Valley, the owner of magical cattle isn't Vellamo but this maahinen Lady. I guess it's understandable, as those Finns are close to the Sámi, and Sámi folklore puts a larger emphasis on similar creatures they call gufihtar.