WHY???
Soap, water and oil are all made up of molecules. Some molecules are hydrophillic, meaning they are attracted to water, and some molecules are hydrophobic meaning they are repelled by water. Oil and water don't mix right?
Well that's where soap comes in. Soap is actually a very long molecule that has one hydrophillic end and one hydrophobic end. The water sticks/bonds with the hydrophillic end and the oil sticks/bonds to the hydrophobic end. Two opposing molecules with the soap in the middle.
As the water is rinsed away, the soap sticks to the water, and the oil sticks to the soap. Voila! Clean!
That's what's happened in the jar. The jar with just oil and water quickly separates. In the jar with the soap added, however, the oil and water stay mixed together for much longer.
Note: For a more advanced explanation (with diagrams and everything) check out How Does Soap Clean from About's Guide to Chemistry.
