The extracts are made from the same steeped malts they're named for. They're not literally "colored", in the sense that something was added to them. They're just concentrated.
Liquid extracts are simply boiled down into a thick syrup.
Dried extracts are made from the hot wort sprayed one layer at a time and are dried into a powder. That's why they cost more, more work. I find the convenience of not having to watch it as closely as Liquid, as it floats rather than sticking to the bottom of the pot, worth an extra dollar.
Base malts have to be mashed in order to convert the starches to sugars. Specialty grains, have already had that done in their roasting. They don't just add color they add their flavors and more sugars to be fermented. If you crack open crystal/caramel malts, they're shiny because their sugars are crystalized.
You don't need "base malts" to brew beer. You'd get all the sugars you need from specialty grains if you wanted replace your base malts with roasted malts.
The only thing you wouldn't be able to do is use additional grains like rice, rye, or particular wheats, unless they were also roasted malts. That's because the specialty grains no longer possess the enzymes that are needed to break down malt proteins and convert starches to sugar.
Getting back to the extracts now. Nothing apart from turning wort into a convenient condensed form are done to extracts. If you add just the extract to water, once it begins to dissolve it smells and tastes exactly as the grains do when brewing.
Not everyone has the space or money to start fully mashing. Also there's a fair bit of study needed before beginning. Partial mashing with specialty grains gives you a taste, but it's far less complicated than the actual mashing process. And cheaper. And faster if you simply want to brew your beer without having to bother with the science of mashing.
Extracts allow you to beef up your beer with minimal effort, specialty grains give you full creative control of your beer apart from adjuncts like wheat, rye, etc.
Also with extracts if you simply wanted to make an easy simple beer, or were being completely lazy. You could just throw your extracts in the pot, use some whole leaf hops in a hop sack. Once the brewing is done, and the wort cooled dump it right in the fermenter with little mess to clean up. Apart from rinsing.
And that's the point of "colored" extracts.
