Hummingbirds can rotate their wings backward, which creates downward 'lift' and backward 'thrust'. By alternating flapping their wings forward and backward, the up and down forces and forward and back forces cancel each other out, so the hummingbird hovers in one place. It can hover long enough to suck out all the nectar it needs from a flower. It's only male hummers that have the brilliant iridescent throat feathers. They use these to display to one another.
Females find it attractive, and other males are repelled.
Male hummers are VERY feisty and territorial and constantly bickering with one another, and the red feathers are part of this territorial display. So they have two functions-attracting a female and defending their territory. The brilliant, iridescent colors of hummingbird plumage are caused by the refraction of incident light by the structures of certain feathers. Like any diffraction grating or prism, these structures split light into its component colors, and only certain frequencies are refracted back to your eyes. The apparent color of any particular part of a feather depends upon the distance between the microscopic ridges in its gridlike structure.