When we want to colour something, we normally add a coloured substance to it. The substance could be paint, make-up or crayon; all such pigments rely on coloured particles. There is a completely different way to "make" colour. Remember back to school science - white light can be divided into its coloured components by shining it through a prism. Different colours of light are bent at different angles, and you get all the colours of the rainbow. Both techniques for producing colour are found in bird feathers.
Yellows, reds, blacks and browns are all produced by pigments (coloured particles) in the feathers. Some greens are as well, though some, along with blues, are produced by the prism effect, known as structural colouration. The (apparent) colours are created when light enters a feather and gets refracted (bent) and bounced through a complex system of cell surfaces within the feather barbs.
A Blue Jay's feathers are not really blue at all. If you get a chance to look at one with the light coming from behind it instead of in front of it, you will see this. But when light enters one of its feathers from the outer surface, it gets refracted just enough to allow only blue light back out. Therefore, we see the Blue Jay as being blue.
Iridescence is another trick of light. We see it as a shimmering of colour on some birds' feathers. Notable examples of this are the red throat feathers (gorget) of the Ruby-throated Hummingbird and the glossy purple head of the Common Grackle. Light enters these feathers and interacts with the cell membranes as described for the Blue Jay, but also with a black pigment called melanin. If you watch a hummingbird long enough, you may notice that its throat feathers alternate between the shimmering ruby-red, and black, depending on your angle of view. When you see the gorget in the light, it appears red. When it is in the shadow, it appears dark - the colour of the melanin granules embedded within the feathers.