Since the 1960s, it has been known that the Earth's continents were subjected to glacial action between about 750 million and 580 million years ago. Paleontologist W. Brian Harland pointed out that contemporary glacial till deposits can be found on all continents, and first proposed that the Earth must have been in an ice age at this time. The problem is that they are found on all continents; even during the worst of the Ice Age just past, ice was still uncommon in equatorial continents. At first the then-new theory of plate tectonics seemed to offer an out, but in fact made the situation worse: studies of the magnetic orientations of the rocks of the period showed that the continents were clustered around the equator rather than being near the poles as might have been hoped.
The Snowball Earth theory argues backwards from the documented existence of tillites dropped by these glaciers, to suggest that the Earth must have frozen over. The mechanism by which it did so is still mysterious, but one suggestion is that the presence of the at-first ice free continents at the poles enhanced the natural process of carbon dioxide reabsorption through the erosion of silicate rocks, reducing the greenhouse effect and making the Earth colder until it reached a runaway point. However, the mechanism by which the Earth would unfreeze (as obviously it has to have done if it did freeze at one point in the past) would leave distinctive traces.
Geological formations which "Snowball Earth" proponents point to as evidence of the hypothesis are:
Eventually enough CO2 would accumulate from volcanic eruption that the oceans around the equator would finally melt, which would produce a band of open ice-free water, much darker than highly-reflective ice, with a characteristically lower albedo, which would absorb more energy from the sun. This would in turn heat the Earth more, melting more water to absorb more light, and so on. This positive feedback loop would melt the ice in geological short order, perhaps less than a millennium.
However, the carbon dioxide levels would still be two orders of magnitude higher than usual. Rain would wash it out of the atmosphere as a weak solution of carbonic acid, which would turn exposed silicate rock to carbonate rock, which would then erode easily, wash into the ocean and form deep layers of carbonate sedimentary rock. Thick layers of exactly this abiotic carbonate sediment can be found on top of the glacial till that first suggested the Snowball Earth.
Proponents of this theory also point out that the frozen period may have ended only a few million years or so before the beginning of the Cambrian Explosion, at the beginning of the Vendian period. While not evidence per se, they consider the apparent sudden appearance of multicellular life suggestive of the removal of some great environmental stress holding life back, and propose that the deep freeze was the stressor.
Another Snowball Earth has also been proposed for the first known ice age, 2.3 billion years ago. There the proposed mechanism is the first appearance of atmospheric oxygen, which would have absorbed any methane in the air. As methane is a powerful greenhouse gas, and as the Sun was notably weaker at the time, temperatures plunged. The evidence here is weaker, but a layer of iron-rich rock can also be found from this time.
One competing, less-radical theory to explain the presence of ice on the equatorial continents was that the Earth's axial tilt was quite high, in the vicinity of 60°, which would place the Earth's land in high "latitudes". An even less severe possibility would be that it was merely the Earth's magnetic pole that wandered to this inclination, as the magnetic readings which suggested ice-filled continents depends on the magnetic and rotational poles being relatively similar (to be fair, there is some evidence to believe that this is the case). In either of these two situations, the freeze over would be limited to relatively small areas, as is the case today, and severe changes to the Earth's climate are not necessary.