As you say, this is a village on the Welsh island of Anglesey. The name is mostly a made up one. Thie village did not originally have such a long name. Instead, much of the name was made up so that the village would have a very long name and could gain publicity through having that name.
The name itself is said to mean "St Mary's Church in a hollow of white hazel near the swirling whirlpool of the church of St. Tysilio with a red cave."
The name was not totally made up. The village already had a pretty long name, which was--and still is--Llanfair Pwllgwyngyll. That part of the name meant "St Mary's church in the hollow of the white hazel."