I've only ever caught a glimpse of a blue jay out of the corner of my eye as a flash of blue. I have, however, had plenty of opportunity to watch Steller's jays. Instead of the blue and white of a blue jay, a Steller's jay is black and blue and every bit as pretty. The blue made in these jays' feathers uses the same principle as the blue sky.
In 1810 Goethe explained blue skies as follows: “If the darkness of infinite space is seen through atmospheric vapours illuminated by the day-light the blue colour appears.” So, the colour comes from some mechanism within the atmosphere during the light of day. (I really like the phrase 'darkness of infinite space.')
Fast forward a few years to John William Strutt (1842-1919), also known as Lord Rayleigh, who was the first to describe the actual mechanism that makes the sky appear blue. He also studied the dynamics of seabird flight, so I'm assuming he often looked off into the sky. Anyway, the effect is called Rayleigh Scattering.
Absolutely tiny particles, like water drops and dust, can be so small they reach a point (about a tenth of the wavelength of light) where light will bend around the particle. The bent light is then scattered differently than it would be for larger particles, in that shorter wavelengths (like blue) are more strongly scattered than longer ones (like red) so we end up seeing the blue. So why not violet, as its wavelength is shorter than blue? It turns out our eyes are just more sensitive to the blue.
Blue feathered birds like blue jays also use Raleigh scattering to get their blueness. Within the structure of their feathers are transparent cells full of tiny particles and pigments. The pigments absorb the longer wavelength colours while the particles scatter efficiently scatter the blue light. To out eyes, these birds look blue.
If you find a blue jay's feather, take care with it because this structure is fragile. If it got crushed the blue colouring would vanish.
Update 26 November 2010 - I didn't quite get this one right, check out here for the start of a better explanation.