Natural selection explains adaptation. That's extremely important and extremely interesting but it's only a small part of evolution. Random genetic drift, which Darwin does not get credit for, explains much more because more of evolution is due to drift than to adaptation.In the Comments, Carl Zimmer wonders, "How are you weighing selection and drift? What's the criterion to decide one process more important than the other?"
The contributions of Charles Darwin are enormous. That's why he gets credit for being the greatest scientist who ever lived. It does a disservice to his achievements to exaggerate them in celebration of the 150th anniversary of the publication of Origin of Species.
I've answered that question many times. I count up the number of fixed nucleotide substitutions that have occurred in a particular gene lineage then I try and decide which ones are adaptive and which ones aren't.
In all cases the non-adaptive mutations seem to vastly outweigh the adaptive ones. Thus, random genetic drift is much more common than natural selection as a mechanism of evolution.
It's shame that Richard Dawkins has given much the same answer in some of his writings but he then goes on to claim that the only interesting part of evolution is adaptation so random genetic drift doesn't even count as evolution.
What's interesting to Richard Dawkins is not the only way to define evolution. I happen to be very interested in the kind of evolution where selection is irrelevant. This is the domain of molecular phylogeny with its approximate molecular clock that cannot be explained by natural selection.
I wish Dawkins would add a note to every article he publishes making it clear that all of his statements are based on the premise that evolution is defined as that which is interesting to Richard Dawkins.