I'll be happy to answer your questions, John.
What is memory? What are memories? Memory is how neurons encode and store information for us to later be able to recall. The purpose of memory, of course, is that our ancestors evolved it because it is advantageous for survival; being able to remember where to find food or hide from a predator is generally a good idea. The hippocampus is the primary part of the brain active in memory; once a memory is encoded, which occurs whenever we pay attention to something unless some impairment is in play, it then spends time in a "consolidation" phase. No one really knows how long consolidation lasts, estimates range from days to months based on various data and measures. However, at all times during this phase, the memory is subject to permanent erasure, if it is deemed useless or expendable by the brain; most mundane events meet this fate, as there is only so much available space, so it is necessary to be selective. Once a memory is fully consolidated, it is mostly safe from loss barring brain damage, and is routed to various areas of the cerebral cortex depending on the modality; visual memories to the visual cortex, memories of thoughts to the prefrontal cortex, etc. Associations and pathways form between these brain areas to link the different aspects of one memory, so that when one is recalled, it usually triggers the whole experience.
Now, bringing PLM theory into the equation, it seems that at some unknown point in consolidation or permanent storage, at least some important memories are backed up in an immaterial medium that is indestructible and independent of the brain. Therefore, the death of the brain does not seem to effect them, and they can be carried seamlessly into a new brain and body. It is hard to comprehend the exact process that leads to this, but given the evidence, I cannot deny the reality of such a nonphysical memory bank. I think it's easy to compare to a computer; when you die, all your data is erased, like a computer's is when its hard drive breaks, but if you back up your computer's data to an external repository before that happens, you can retrieve it all again when you buy a new hard drive. For us, this immaterial backup is what we could call our soul. In reincarnation, the soul, when entering a new body, only has to implant its memories of the PL into the brain, and they are then consciously accessible in the new life, giving us what we observe in PLM children.
What triggers memories? Why/how do we remember them? One way for us to recall something is to do so voluntarily, if it is prominently accessible; for example, when needing to remember where one left a credit card, or how to spell a word in a spelling bee, we willfully and effortfully recall the information. The neural mechanisms of free will are not known, and many neuroscientists claim there is no free will at all, and all our actions are externally caused in some way; I am not one of those. Other methods of memory recall are cued, and the majority of child PLM cases begin this way. Most cues that trigger memories simply involve encountering a stimulus that serves as a reminder of a prior experience, and these reminders have the power to trigger anything from a very recent memory, to something you may not have recalled in many years, and forgot you even still remembered by that point. The great neuroscientist Wilder Penfield, a very big believer in reminders, hypothesized that our memory bank is in fact capacious enough to store every single relevant or unique event we've ever experienced, except for those in infancy, and if we encounter just the right reminder, any of these experiences can be spontaneously recalled. He came to this conclusion when he hooked up electrodes to the cortices of epileptic patients, trying to diagnose the location of the tissue causing their epilepsy. Sometimes, when Penfield sent a small charge through, the patient would report recalling a random, specific memory, often one so obscure that they had completely forgotten they had it. This led Penfield to infer that if such random, obscure memories persist so permanently, it is likely that all relevant events are stored, and that a precise reminder could produce the same effect as his electrodes did. Ever since his work, it has been agreed that our memory storage capacity is much greater than we once thought.
In the context of PLM's, most initial recall is cued. Since our brain prioritizes more salient and immediate information to be more easily recalled, and since it's been a few years since the child reincarnated, the PL memories are not usually at the front of the mind until they are externally triggered. That is not to say this is always the case; sometimes kids just start talking about PLM's as soon as they have the ability, and for no discernible reason other than to express themselves. Once the memories are at the forefront, however, they appear to behave like any other memory; the child almost always perceives an unbroken continuity between the memories of the present and previous lives, and they find nothing remarkable about them in most cases. Given these patterns, it's incredibly hard to deny that PLM's stem from the same source and feel the same to the child as any ordinary memory, and using neuroimaging to demonstrate they are of the same substance would only seal the deal. This is where I believe modern science and PLM theory intersect cleanly. Of course, if our current science is as valid as we hold it to be, everything that exists and is true ought to connect with it, and reincarnation is no exception to that.
tl;dr - Memory is the neurological process of encoding, consolidation, storage, and recollection, and primarily involves the hippocampus in the first two stages and the cerebral cortex in the last two. PLM's seem to involve some sort of subsequent backup to a nonphysical storage medium that persists beyond death, that being the soul.
Memories can be recalled voluntarily or by triggers, which usually consist of well-placed reminders that can spontaneously trigger even very obscure memories, and direct neuronal stimulation has also been proven to do the trick the same way. PLM's are mostly cued, but once recalled initially they can be voluntarily invoked like any other memory.
For once, I avoided saying anything contentious in this post!