I'm one of the 8% of all men who are colour-blind, most of us with an inability to distinguish red from green. This isn't a major problem but it is a nuisance when designers don't take it into account, using indicators which change colour from red to green (e.g. battery chargers), or PowerPoint presentations with green text on a red background.
The other 92% of you must find it hard to imagine what the world looks like to us. To me, grass looks bright orange, blotting paper is grey, and the colour red just doesn't leap to my attention the way it probably does to you.
Colour-blindness is a physical problem with the eye, as is short-sightedness, so it's not a matter of just not having "learned" the colours - we actually cannot perceive the difference between some of them. Subtle differences in colour perception may be quite widespread - people with "normal" colour vision sometimes start by testing me on the colour of this, the colour of that ... and before long are arguing with each other over a particular colour.
To imagine what it's like, try turning down the "colour" setting on your television or monitor until there's almost no colour on the screen. To begin with, everything looks very black and white, but in time your brain adapts and the colours appear to come back, or at least you don't notice they're missing. But now you don't have very good sensitivity between them, so you might start to confuse an greenish red with an orangeish red, that kind of thing. The world still looks just as "colourful" as normal, but you have lost some of your colour discrimination.
Human eyes have 3 types of colour sensors in them - red, green and blue. For this reason, all the kit we use to capture and reproduce colour (film, digital camera sensors, colour monitors, print media) only needs those 3 colours to trick us into thinking that an image is in "full-colour".

I am a "protanope" which means that
there's something wrong with just the red receptors in my retinas. I'm
not sure if it's that they don't work very well, or they're missing, or they're
just tuned to the wrong colour. To give you an idea what this is like, below
left is a picture I took of the sunset in
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To perhaps make this easier for you to understand, here's a colourful picture of a toy:

The red, green and blue components look like this:



If we just remove the red and keep the green and blue (as I did with the

then I've added back the blue to give this:

It may appear at a glance to be a truly "colourful" picture, but actually it's missing 1/3 of its colour information.
If some people had 4 types of colour sensor in their eyes, instead of the usual 3, then they'd be able to tell the difference between colours that we couldn't, and everyone would seem colour-blind to them.
If you think you might be colour-blind, your optician can give you a simple test. The old Ishihara test is most common - you are shown a series of pictures, each of which consists of a bunch of randomly-sized dots forming a pattern (e.g. the digit "7"), on a background of other randomly-sized dots. The random sizing of the dots prevents you from using shape as a recognition mechanism, forcing you to use only colour. If you can't distinguish e.g. a symbol made of red dots on a background of green dots, you may be a protanope, just like me. Don't worry, it's no big deal unless you want to fly a fighter plane, so just enjoy seeing the world a bit differently from everyone else.

(The true colours of the printing inks used to print the test shown above are different from those red/green/blue colours used by computers, so the above picture isn't spectrally correct, and you can't take this test online).
There are no real cures for colour-blindness. It's understood quite well genetically now, so eventually we'll probably edit it out of the gene pool but for now we are stuck with it.
Meanwhile there are contact lenses which filter the image that your left eye sees differently from that of your right, to try to recreate the missing information. For example if you can't sense red then the lenses might filter out the red from just one eye. Everything will look normal if you look at a green or blue object - both eyes are seeing the same thing. But if you look at a red object, for example a rose, instead of looking "dark" as it did before, it glows in a most amazing way, the result of your brain trying to cope with the fact that it's getting different information from each eye. This is a neat idea and you can try it for yourself if you can find a piece of red filter (hold it in front of one eye for around 5 minutes until you adapt to the light difference). However, a friend who tried the contact lenses said it gave him a headache, probably because it interferes with the eye's focussing mechanism which makes use of the image convergence between your two eyes (if they're seeing different colours, it harder for the brain to know whether this is because your eyes are not pointing in quite the same direction, and/or because the lens in your eye acts like a prism and so different colours focus at slightly different distances.
Even if in the real world you can't be sure what colour something is, at least you can when you're using a computer. A big thank you to the Microsoftie who wrote the software that makes the name of the colour pop up when you're picking colours from the standard Office 8x6 colour palette. And outside of this, please do use the excellent WhatColor shareware application to tell you what other colours are on the screen, or buy the excellent new eyePilot software. You can also use an online tool at Visicheck which alter the colours to improve discrimination according to your particular kind of colour-blindness.
An excellent review of colour-blindness which goes much deeper than this article, with several examples, has now been published here. It includes an online tool to which you can submit any picture and see how it would look to someone with different types of colour-blindness.
Color blind