Why does warm water clean stuff better than cold?

First off heat kills most bacteria so it is especially important for bedding. Heat also expands items so detergent can get into the fabric easier thus clean more effectively.

Next Answer:

From the perspective of chemistry, heat is one of the things that can begin or accelerate a chemical reaction. Laundry detergent is probably more effective if some heat is added because it either starts a chemical reaction, or makes one faster, and thus can do its job better in the limited amount of time provided by a wash cycle.

To make things simpler, the fact that hot water allows for the detergent to dissolve, whereas the soap simply sits on top of the cold water and doesn't do it's job. For example, those who live in the south know that it's easier to sweeten tea while it's hot than when it's cooled off. Just a thought :)