A likely explanation for some ball lightning

Natural ball lightning probed for the first time - environment - 16 January 2014 - New Scientist

I don't think it can possibly explain all ball lightning - such as the well attested cases where small balls have appeared inside houses and even an airplane - but it appears there is a good explanation for one type:

In 2012, Jianyong Cen and his colleagues at Northwestern Normal University in Lanzhou, China, were observing a thunderstorm in Qinghai, China with video cameras and spectrographs. Purely by chance, they recorded a ball lightning event. When a bolt struck the ground, a glowing ball about 5 metres wide rose up and travelled about 15 metres, disappearing after 1.6 seconds.

The spectrograph revealed that the main elements in the ball were the same as those found in the soil: silicon, iron and calcium. The observations support a theory for making ball lightning put forth in 2000 by John Abrahamson at the University of Canterbury in New Zealand.

Abrahamson surmised that when lightning hits the ground, the sudden, intense heat can vaporise silicon oxide in the dirt, and a shockwave blows the gas up into the air. If there's also carbon in the soil, perhaps from dead leaves or tree roots, it will steal oxygen from the silicon oxide, leaving a bundle of pure silicon vapour. But the planet's oxygen-rich atmosphere rapidly re-oxidises the hot ball of gas, and this reaction makes the orb glow briefly.

The theory garnered support in 2006, when scientists at Tel Aviv University in Israel were able to create ball lightning in the lab by firing mock lightning at sheets of silicon oxide. The event in China marks the first time such an orb has been captured in nature with scientific instruments.