Asmat is a remote swamp-and-river region in southwest Indonesian New Guinea. It is not an easy place to visit: distances are wet, slow, and expensive, and most movement between villages is by boat. That difficulty is part of the truth of the place, not a footnote.
The reason to come is Asmat culture. The Asmat people are famous across the Pacific for woodcarving, ancestor poles, shields, drums, and ceremonies tied closely to river life. Agats is the practical base, with the Asmat Museum of Culture and Progress giving the best introduction before you arrange village visits.
This is a specialist destination, but a real one. If you are already travelling in Papua and can handle the logistics, Asmat offers a very different world from the highland treks of the Baliem Valley or the reefs of Raja Ampat.