Depends what you mean by explain.
Evolution is a mechanism to explain how replicators change over time.
In the modern synthesis, it is a very complex collection of systems that had a relatively simple beginning.
If you have something that can replicate in some context; and
If that thing sometimes produces variants (ie replication isn’t perfect, but the result is sometimes different with some frequency); and
There are different contexts in which those replicators can survive; and
The contexts themselves change in some set of dimensions that are different; then
The process of differential survival between variants in different contexts will lead to a divergence between the populations over time.
Lots of different factors are important in exactly how that process works over time.
Understanding the details of the modern synthesis is a process of years, and the main themes can probably be learned in a day. In this sense, everything that Richard Dawkins has written is important to understand at the simplest level. Selfish Gene remains a classic, even if Richard has refused to seriously consider the recursive implications of the work he has done. David Sloan Wilson does a much better job of that – as a good introduction to a subject that to me seems orders of magnitude more complex than even David has written about.
It is a subject that has fascinated me for over 50 years.
My understanding of it is now all based in probabilities and uncertainty, from the uncertainty of Heisenberg, to that of Goedel, from the mathematical notions of infinity and irrational numbers and chaos and randomness to the quantum mechanical notions of chemical interactions, from games theory to complexity theory to chaos and fractals, from deep neural nets to computational theory, from engineering to programming, to a deep interest in all things real, historical, social, legal, philosophical and how everything is related.
For me, with my particular sets of interests and studies, the answer is an easy yes.
The possibilities inherent in the modern synthesis are capable of explaining an infinite array of life, far more varied than we have seen as yet, and it is very different from the popular conception.
For me it is clear beyond any shadow of reasonable doubt that any levels of complexity that are to survive long term must be fundamentally based in cooperative structures. Thus I see the tendency of many today to base their interactions on the competitive and scarcity based values of the market place as a fundamental threat to the survival of intelligence itself. Our systems need to be fundamentally based in cooperation, in a fundamental respect for life and liberty and all the social and ecological systems that make those possible and interesting. We can build as many competitive systems as we like atop such a cooperative base; but if we try to make the base competitive then both life and liberty are at serious risk. The evidence for that is overwhelming to me, and deeply embedded in the structure of the systems of life we observe (if we are prepared to look deeply enough into it).
So yes – for me, evolution explains all life, and it is not a simple notion of evolution based in competition; it is a profoundly more complex notion of evolution where all new levels of complexity are fundamentally and necessarily based in cooperation.
It is evolution that explains both the emergence and the necessity of ideas like morality. (https://www.quora.com/How-does-evolution-explain-morality-and-the-development-of-morality/answer/Ted-Howard-16)
It is evolution that explains why all understanding is necessarily a simplification of something vastly more complex than can be comprehended in detail by any computational entity (human or non-human, biological or mechanical). So all understanding is necessarily wrong in some essential dimensions, and all we can hope for is enough humility to give up our certainties and become less wrong over time.
It is evolution that explains the necessity of simple models in some contexts, and the tendency of many to carry such simplicity to places it really does not belong.
It is evolution that demands of us a respect for diversity (including diversity of understandings), if we are to have any significant probability of surviving long term.