Beltane is one of those cross-quarter days .. the midpoints between the seasons. (Groundhog Day, May Day and Halloween are holidays that derive from these days*). It seems people would make hilltop fires and run their cattle, sheep and goats through them as part of a purifying ritual (I'm sure the animals weren't very amused). People would do the same thing and this tradition seems to have survived in both Ireland and Scotland (especially in Edinburgh).
Claudia Schmidt has a song that has its roots in the sport
One of my old students was into Inkubus Sukkubus and had me listen to this... (your mileage may vary)
Anyway - if you have Gaelic blood (I do) and feel disposed to run yourself or your goat through a fire tonight (I don't), it is your heritage. Of course you can always take up Morris Dancing.
(note that May 5 is the real cross-quarter day, but all of these have a bit of rounding)
*For years I have thought it would be interesting to start a holiday on August 1 that traces to Lammas ... the cross-quarter day that marked the first wheat harvest. It is odd that three of the four days have modern offshoots.