The reason for this is that the size of the soil particles is very different. A particle of sand is much bigger than one of silt, which is much larger than a particle of clay. To illustrate this, I've lined up some items on the windowsill to help you get a visual sense of the differences.
The cherry tomatoes on the left represent the large particles found in sandy soil, the rice (center) is like the much smaller particles of silt and the flour, at right, has tiny particles similar to clay. (Don't hold me to these exact proportions: this photo is just to give you way to think about this.)
Now imagine what happens when it rains. If you have sandy soil, it's like putting the cherry tomatoes in a colander and running water over them. As soon as you turn off the faucet, water runs right through those big pore spaces, leaving just a thin coat of moisture on surface of the tomatoes. If you are gardening in sand, you know this - without organic material added to the soil to soak up and hold onto water, it dries out in no time.
You can think of silty soil as being like the grains of rice. When you run water over rice, it drains slowly, leaving quite a bit of moisture both coating the grains and held in the small spaces between them.
Clay particles behave a lot like flour. They are so tiny that they pack in tightly together with very little space between them. If you pour water on flour, it will just sit there until you mix it in. Once you've mixed it in, however, it is very hard to completely dry it out.
OK, so that's how soil particle size affects water retention. Particle size also matters when it comes to nutrients. Ions of nitrogen, potassium, phosphorous, calcium, magnesium, sulphur, etc. cling to the outer surface of soil particles where they can be taken up by plants. Smaller particles, like silt and clay, have far more surface area per volume than those big particles of sand and therefore can hold a lot more nutrients.
Bear in mind that this is a very simple explanation of soil types. It is enough information to help you make some reasonable decisions about how to improve your soil, which I'll talk about in the next post on soil amendments. But it by no means covers the subject. Healthy soil is more than particles, it includes organic material and many living organisms working together. I strongly recommend that gardeners learn more about that fascinating world under our feet. James Nardi's book, "Life in the Soil: A Guide for Naturalists and Gardeners," is a good place to start.
Remember that unless you are right on a sandy beach, your soil is likely some combination of particles. If you aren't sure whether it is mostly sand or clay, you can do the "squeeze" test. Pick up a handful of moist soil and try to make it into a ball. If it packs nicely into a ball, it has a lot of clay in it. If it crumbles without holding a shape, it is mostly sand.
Wondering how much mulch, soil or compost you should buy for your gardening project? Check out this handy table.
Read part 1 of this series - Here's the Dirt: Introduction