We don’t use this much nowadays — dictionaries usually tag it as archaic or literary — except in the set phrase make the welkin ring, meaning to make a very loud sound.
What supposedly rings in this situation is the vault of heaven, the bowl of the sky, the firmament. In older cosmology this was thought to be one of a set of real crystal spheres that enclosed the Earth, to which the planets and stars were attached, so it would have been capable of ringing like a bell if you made enough noise.
The word comes from the Old English wolcen, a cloud, related to the Dutch wolk and German Wolke. Very early on, for example in the epic poem Beowulf of about the eighth century AD, the phrase under wolcen meant under the sky or under heaven (the bard used the plural, wolcnum, but it’s the same word). Ever since, it has had a strong literary or poetic connection.
It appears often in Shakespeare and also in Chaucer’s Canterbury Tales: “This day in mirth and revel to dispend, / Till on the welkin shone the starres bright”. In 1739, a book with the title Hymns and Sacred Poems introduced one for Christmas written by Charles Wesley that began: “Hark! how all the welkin rings, / Glory to the King of kings”. If that seems a little familiar, it is because 15 years later it reappeared as “Hark! the herald-angels sing / Glory to the new born king”.