Colored lights are one of those things where some people don’t really see any purpose to them and others find dozens! 
The first use, of course, is ambiance. Fancy light effects that really get your attention. Or just holiday lights for Halloween and Christmas. 
One of the most popular uses with home automation is as alerts. Have a light turn blue when the mail arrives, pink when the laundry is done, green when there’s someone at the door… Different people find different uses.
When it comes to color temperature (cool white to warm white), some people are very sensitive to this and really appreciate being able to set the color temperatures. Cool white for precision work, warm white for relaxing.
Some people like to use what is called a circadian light where the color changes during the day to match the natural sunlight changes outdoors.
But for other people, all of this is moot: they just want dimmer control, and that’s it.
Anyway, the following thread is very old, so a lot of the devices being discussed have since been discontinued, but the use case ideas are all still relevant if you’re interested.