Many detergents are amphipathic - that is to say, they have hydrophobic (water hating) and hydrophilic (water loving) areas. As a result, part of a detergent likes to be in the water and part of it doesnt. This is why detergent can be used to wash oily stains. The hydrophobic part of the detergent sticks to the oil (see hydrophobic effect) while the hydrophilic part stays dissolved in the water. If enough detergent molecules stick to a droplet of oil, they can pull it off and carry it around in the water, allowing it to be washed off.

But, this is a node about micelles. Micelles are structures that detergents spontaneously form in water. A group of detergents stick together with their hydrophobic tails, forming a ball where all the tails are on the inside and all the hydrophyllic heads are on the outside. The result looks like an inside out KooshTM:


             o
          o  |  o
           \ | /           o  hydrophillic head group
         o--- ---o         |
           / | \           |  hydrophobic tail
          o  |  o
             o

The two dimensional cross section above shows how the hydrophilic head groups are all facing out towards the water while the hydrophobic tails are packed inside the center. The micelle is a sphere of detergent with the heads packed together tightly enough that little water penetrates into the center of the ball. Micelles may form spontaneously above a certain concentration of detergent (known as the critical micellar concentration - the CMC) or they may form at lower concentrations in the presence of a nucleus, such as a drop of oil. You can imagine a drop of oil sitting in the center of the above micelle, with the detergent molecules projecting out from it in all directions. Detergents form micelles more readily than lipids because the extra tail makes it difficult for lipids to pack into a ball. Lipids tend to form large planar layers rather than tight balls.