What mechanism could explain the diversity of life?
*note, I will throughout this refer to the 'Darwin Finch' to use as an example of how diverse life can get from your premise in your question= 'diversity of life'.
When we define 'survival of the fittest' (or evolution) is what it says on the tin, the best organism which is more fit to be in the environment it finds itself in, will survive.
'Speciation' is defined as the formation of diverse organisms via 'survival of the fittest', which were once able to interbreed and now are too different to, I will explain this more in my Darwin Finch example.
'Environment', by environment and everything about it, from the other organisms there to its climate.
Now to show why these 3 are most important via the Darwin Finch.
The Darwin Finch is an bird 'indigenous' to the Galapagos Islands, they are thought to have arrived there a couple thousand years ago after their flock was blown off its migratory course by a storm and to Galapagos.
This flock was separated over these different islands, and they found themselves in many different sorts of environments with varying food sources, e.g. insects, nuts, fruit.
Those in the flock which had the better beak characteristics to eat that island's main food source, be it fruit or nuts, would survive better (due to being fitter for that environment) than those without those desired beak characteristics, and the latter would eventually die out or their characteristics disappear as they bred.
Over time, these birds would interbreed more and more on their islands until speciation would occur, due to the physical barriers of sea between these islands, and many are very genetically different to their ancestors.
These finches were crucial to Darwin's eventual theory of survival of the fittest (evolution), which brought about this diverse range of birds in a relatively small area (8,010 km²),
I hope you can see why and how this is replicated else where (e.g. Red Squirrels in Britain with no pox resistance, Grey Squirrels in America with pox resistance). If organism's characteristics are good, it will survive better than it's counterparts.
Hope this helps.