Evolution is the way in which groups of organisms change over time, usually in response to changes in their environment. The way in which this change is carried out is by a process known as "natural selection," where those organisms that are best able to survive go on to reproduce, and pass down to their offspring the same traits that allowed them to survive. Sometimes, an organism's DNA-the code inside its cells that "programs" the organism's body-changes; this is called a mutation. Some mutations are harmful (and the organisms that have those mutations do not tend to survive to reproduce) but other mutations can have little effect, or even be helpful: these organisms will usually survive, and pass their mutations on to their offspring.
In most cases, mutations will not cause any overall changes in a group of organisms. It's only when there is a change in the environment where the organisms live that evolution starts to play a part. As the environment changes, the organisms that are best able to adapt to the changes-those which have the most beneficial mutations-will survive; the ones that aren't able to adapt will usually die out. Over many generations, a group of organisms that is forced to adapt to enough change may sometimes become a completely different kind of organism: biologists call this "speciation." That word may look familiar-it's related to the word "species," which is how a unique kind of animal is categorized.
Evolution is sometimes called a theory, which is at the same time correct and misleading: the fact is, the theory of evolution is only one part of the study of evolution. The theory of evolution is the model that scientists have built to explain how evolution works, and predict how organisms will change in the future-for instance, how a type of bacteria will develop resistance to a particular drug.
Evolution doesn't try to explain how life began (that's a different field of study, called "abiogenesis") or try to be an absolute truth. Evolution is a tool used to explain how organisms change, and to try to understand how they will change in the future. It's the best tool, so far, that has been found for making these predictions; chances are, it will remain the best tool for the job for many years to come.