What explains the presence of vestigial organs, like the tiny, useless, legs of many snakelike lizards, and the vestiges of a pelvis in pythons?

These are remnants, and the term "vestigial" is not a bad one because they are a reflection of existence of such structures for a true purpose that is understandable and clearly significant. We would say "purposeful" because all were designed initially during the creation of the life forms. Many, many times organisms have been modified by us to adapt them, repurpose, and rework them to use them and deploy them in a variety of circumstances, and the environmental niche they are optimized for may require further tinkering to adapt them to conditions somewhat different, but enough to obviate the need for certain anatomical features and functional capabilities. That was the case here, that a variety of organisms were re-engineered to serve in various ways, in various environments, and as a consequence of the prior genetic determinants, there were some features that were not critically required but still expressed to some degree. And, in this case, giving rise to the vestigial organs that seem to be purposeless and, in fact, do not contribute in a way to benefit the life of the organisms, but yet are present seemingly as a leftover echo of perhaps a prior organism whose genetic characteristics were modified over time via evolution. This is not terribly far from the truth but was not evolution through natural selection, it was evolution through intelligent design to take the genome of an organism and redeploy it through some alteration to optimize things in a certain way to create new varieties of life and to help it flourish in a somewhat different environmental setting. So there are many, many examples all through the various life forms showing similarities and what appeared to be an evolution of many organs and tissue elements when, in fact, they are simply variations that were created directly with some reworking of things, and there may well be created thereby the illusion of an evolutionary progression from simple to complex, or containing limbs and then being devoid of limbs, and so forth. Sometimes things are preserved genetically that are not essential and then will be apparent in the animal and its appearance, and appear inexplicable. There are examples of things that have been altered purposefully by interlopers as well and particularly true for human. Those alterations were not natural but were orchestrated to happen, in particular, to cause disarray and damage to function, so there are multiple reasons for oddities of this sort. What we would say is: "Make the most of what you have and understand that when situations give rise to organisms with features that seem to be inefficient and serve no purpose, that may also be just from a human perspective as you are not appreciating the creature in question and how it carries out the life function and all that is required for every necessity it must obtain in some way in order to survive. There are many plans, and many variations of those plans, but they are all designed and a form of experimentation as well. The feedback from these efforts has allowed further exploration and, in effect, an evolution of our ideas and thinking."