Sulfates are a surfactant, and in layman's terms (with as little complicated chemistry language as possible) and surfactants help increase the surface area of water.  This basically means that water is able to spread more and cut through things that would otherwise oppose the spread of water, i.e. oil.  Our scalp and skin are loaded with natural oils, which is why sulfates are added.  Sulfates however, are very harsh to our skin, and cause it to enter a viscious cycle in which our skin releases more oils to combat the sudden and harsh drying effect they have.  This means your skin is working twice as hard to moisturize itself, and you notice it on days where you don't wash with a sulfate product and realize you're feeling really greasy.

Without sulfates, the cleansing agents need a bit more work to do the job (a 2nd wash) but ultimately this is far less damaging to our skin than loading it with chemicals.  Our skin absorbs everything we put on it, if it didn't there wouldn't be medicinal patches.  Therefore, try not to load your skin with too many harmful chemicals, because in the end they're being absorbed into your body.  Sulfates and parabens are some of the worst we can put on our skin, so I look for sulfate free and paraben free shampoos, conditioners, moisturizers, cosmetics, and sunblock.

I'm going to try that Kiehl's shampoo now, still haven't found one I love.