When self reproducing organisms divide, they duplicate their genes so each new cell has a copy. This duplication can have errors, which means there is at least some low level chance of a mutation. There can also be mutations before duplication, say from radiation etc. But these changes are pretty slow. However, lots of bacteria etc can either transfer bits of DNA to each other, or they can pick up DNA from their environment. This, along with quick reproduction times, means they can evolve relatively fast
There is still some random variation in genes through mutation but in general, sexual reproduction has proven to be extremely advantageous and sexual creatures vastly outnumber asexual ones. What very few exclusively asexual creatures remain have indeed evolved at a geometrically slower rate and are much the same as they were millions of years ago – those particular surviving configurations just proved to be very effective.
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