Light
Light, particularly white light, is a blend of different colors or wavelengths of light. Incandescent light bulbs offer a broad spectrum of light, including more invisible infrared light than visible light (making them less efficient). LEDs produce a very narrow band of color. White LEDs produce very bright blue light, but by adding yellow phosphor to the surface of the LED, a yellow wavelength is mixed in and the resulting light appears white.
Tints
Different LEDs and different types of lights produce varying tints of light. Small differences in the production of LEDs can produce differing tints. The LEDs are evaluated and grouped in bins based on the resulting tint. Most LEDs have a cool white tint which is slightly blue. However some people prefer a more neutral light. Because more phosphor is added to obtain a neutral tint and the phosphor blocks some of the blue light, neutral LEDs are not as bright as cool white ones. Warm white has more of an orange color and is even less bright, adding yellow and other colors of phosphor. Tints are often measured by Correlated Color Temperature, which assigns a value in degrees Kelvin to different tints, from 5700K for cool white to 2700K for warm white, with 4500K being neutral.
Color Rendering Index (CRI)
A measure of the quality of light is how well it renders colors across the spectrum. Some types of light emit only a narrow wavelength, making all colors look about the same. Sodium vapor street lights might have a color rendering index value of only 25. Many cool white LEDs and compact fluorescent bulbs have a CRI of about 60-70 due to their light having only a couple of spikes at certain light frequencies (colors). Incandescent light and sunlight have CRI values of the maximum of 100. There are "high CRI" LEDs with values starting around 80 and going up into the low 90's. CRI is measured at a certain temperature since a red object will have a different appearance under a lower CCT incandescent lamp than higher CCT sunlight, even though both light sources have a CRI of 100. There is a good article here about CRI, in addition to the more technical article in Wikipedia.
High CRI LEDs typically have a warmer tint, though not always. And a warm tint does not necessarily mean the LED is high CRI.
Light Output
A light source has a total amount of output measured in lumens and a the intensity of the light at a point which is measured in lux. The intensity of the light drops with distance. See Light Output Measurements for more information on this topic.
Light Colors
Though most people prefer white light, special situations arise where a color of light is desired. Astronomers and others who want to maintain night vision and see details like maps or notes often use red light. Night vision is best preserved using blue-green light as seen in night-vision equipment. And blue light is supposedly good for seeing blood at night.