John the Baptist – in Danish: Johannes Døberen; the name Hans is derived from Johannes – is said to be born six months before Jesus (according to Luke 1), which is right around now (according to the date of Jesus’ birth set by… Who??… Oh well).
I’d love to explain to you the traditions of Denmark in my own words, but for once I think that another source is actually doing a better job:
It has been celebrated since the times of the Vikings by visiting healing water wells and making a large bonfire to ward away evil spirits. Today the water well tradition is gone. Bonfires on the beach, speeches, picnics and songs are traditional, although bonfires are built in many other places where beaches may not be close by (i.e. on the shores of lakes and other waterways, parks, etc.) In the 1920s a tradition of putting a witch made of straw and cloth (probably made by the elder women of the family) on the bonfire emerged as a remembrance of the church’s witch burnings from 1540 to 1693. This burning sends the “witch” away to Bloksbjerg, the mountain ‘Brocken’ in the Harz region of Germany where the great witch gathering was thought to be held on this day.
Holger Drachmann and P. E. Lange-Müller wrote a midsommervise (Midsummer hymn) in 1885 called “Vi elsker vort land…” (“We Love Our Country”) that is sung at every bonfire on this evening.
Source: Wikipedia: Midsummer –> Denmark (as of June 24th 2010 @ 2:50 AM)
Additionally, I remember many a midsummer bonfire where a firecracker has been put in the witch, making her scream as she was burned.