1. The first gradient is a linear interpolation in gamma-corrected RGB. This is likely considered the most 'correct' gradient.
2. The second gradient is the naive gradient, not correcting for display gamma. See how nasty and dark it gets. Ugly.
3. The third gradient is the gradient in CIE L*a*b* space, a perceptually uniform colour space (supposedly). This is an approximation of what should look the smoothest transition to a person.
For more information about Colour and these gradients, check out Poynton's Colour FAQ.