One of the most difficult things to explain in biology is the appearance of sexual reproduction. Lots of organisms reproduce asexually and they do just fine, so why did such a complex process as sexual reproduction arise and how did it come about through purely natural processes?
In order to reproduce sexually an organism has to, inter alia, develop meiosis, it has to develop an entire suite of hormones, organs and anatomical structures, and it has to develop behaviors that trigger hormonal responses in its potential mates.
To catch a glimpse of the sheer complexity of just one aspect of this astonishing means of reproduction watch this marvelous five minute animation of mammalian (human) fertilization and consider all of the engineering that had to go into designing this process. Then ask yourself what the chances are of such a phenomenon being produced by mindless, blind and purposeless coincidence.
If any of the numerous structures or complex chemical reactions in this process failed to develop fertilization would either be impossible or exceedingly less likely.
Any naturalistic account of the evolution of this phenomenon would be indistinguishable from a miracle, but since naturalism excludes miracles the appearance of sexual reproduction is, for the naturalist, a mystery. On the other hand, the alternative to naturalism, theism, explains the appearance of sexual reproduction as the consequence of the purposeful action of an intelligent agent who designed this process with goals in mind.
When we watch the video it certainly seems that everything that occurs in the fertilization of a human ovum is goal-directed, purposeful and extraordinarily improbable on the naturalistic assumption that its evolution was a fortuitous accident.
For a fuller explanation of the content covered by the video check out this piece at Evolution News.