Morris dancing is incredibly old, earliest records are from the 15th century and even then it was just another part of everyday life. It’s origins may be completely lost but this doesn’t stop a variety of theories, so here's a plausible story:
It’s an old English custom. No-one knows why it started, just that it's been around for at least 600 years, and there are similar traditions in other European countries and regions, such as Romania, the Balkans, and Spain. The name 'Morris' may be a corruption of "Moorish", a term brought back by soldiers from the crusades. There is no evidence that it has pagan origins or that it was part of a fertility rite. Nowadays it's mostly done because, well, we're Morris men and it would strange to be a Morris dancer without dancing the Morris. It keeps us out of the house too, though unfortunately not off the streets.
As far as we are concerned, the origins don't matter, we do it because it is fun and gives us the chance for some not too strenuous exercise in convivial company.
For a deeper description of Morris dancing you can do a lot worse than to look at the The Morris Ring website.
This is an organisation to which the Men of Wight belong, which brings together male Morris sides from all over the civilised world, even the bit on the wrong side of the Solent. The Ring's site tells you all you might want to know about the Morris, so rather than repeat it all, just follow the link.