Define the theory of evolution. How does it influence Wells' vision of the aliens in the novel?

The theory of evolution simply says that species change over time.  I believe that the intent of your question is asking about Darwinian evolution.  

Darwinian evolution hinges on the concepts of "Survival of the Fittest" and "Natural Selection."  In a nut shell, a more fit individual is more likely to survive.  Because it is surviving, it stands a greater chance of passing on its genetic information.  Thus its progeny will likely inherit whatever made that individual more fit.  Consequently the entire species begins to slowly pass on and inherit that trait.  What makes an individual more fit?  Adaptation.  An adaptation will increase an individual's overall fitness, thus ensuring better chances of survival.  Hence, the following line of thought.  Nature will "naturally select" which species or individual will survive based on adaptations that influence the overall fitness of an organism or population.  

Darwin's theory does apply to the aliens in the book War of the Worlds.  It applies most notably to the end of the book.  The aliens have all died, because they were exposed to Earth's bacteria population.  The aliens had no immunity to the harmful bacteria, because they were not given sufficient time to develop the necessary adaptations; therefore, the aliens were naturally selected to die out, because they were not the fittest organisms around. 

These germs of disease have taken toll of humanity since the beginning of things—taken toll of our prehuman ancestors since life began here. But by virtue of this natural selection of our kind we have developed resisting power; to no germs do we succumb without a struggle, and to many— those that cause putrefaction in dead matter, for instance —our living frames are altogether immune. But there are no bacteria in Mars, and directly these invaders arrived, directly they drank and fed, our microscopic allies began to work their overthrow.