On the one hand, we think that the fact that a theory T1 allows for "better explanation" of a certain phenomena than T2, gives us reason to believe T1 rather than T2 is correct. It's obvious (if not particularly explanatory) reason to prefer one theory to another that it "does a better job of explaining the data"!
On the other hand, we think that a better explanation can be one that better helps human beings "grock" patterns in the behavior of physical systems which may be mathematically very complex. Given human psychology, attention span etc. a simple ceterus paribus statement about struck matches tending to light can be a better explanation than an explanation that appeals to more specific details. To choose a more extreme example, even if there were a completely successful theory of microphysics, most people feel we would still have an explanatory task. We would still want elegant theories that told us about general high-level patterns in how the microphysical facts would evolve forward through time. (e.g. the ideal gas law, biology and maybe psychology and economics).
But now here's the problem: do we really think that the fact that a theory T allows for nice tractable/human-grockable explanations of high level phenomena makes it more likely to be true? For example:
I find "consider a spherical cow" style economics explanation, or "consider philosophers building up society from a state of nature" style early modern philosophy explanations way more attractive, satisfying, and easy to remember than explanations that cite lots of boring contingent historical facts. But this doesn't really make me feel that these explanations are more plausible, or getting at the heart of matters more.
I mean, I wouldn't be surprised if primate intelligence is optimized for avoiding getting double crossed by other monkeys, and making practical plans etc. so we like explanations better if they relate the explananda to these things (i.e, people with plans). Indeed don't we actually find this with explaining a phenomenon to people in different disciplines- that people familar with different areas find different explanations more satisfying?
We like explanations where lots of correct consequences "fall out immediately" from a tiny theory. But what seems to fall out immediately (vs. just be an ugly mathematical consequence) may well depend on how familiar you are with inferences of that kind. And folk (belief/desire) psychology is something we are *all* very familiar with from daily life. Hence, when someone says "this electron wants to escape the other electron" or "countries covet land", we have lots of immediate ideas about what behavior should follow from that, because we are experts at drawing consequences from belief desire psychology, and then we just convert these consequences back to the task at hand.
But surely allowing for nice parallels to common problems in monkey social climbing, is not a feature that has much to do with genuine theoretical elegance/ how likely a theory is to be correct.