I have to admit that some of the jargon out there eludes me. I'm not a techno-whiz, AT ALL, and maybe that's a bad thing here.
That said, can someone point me to a succinct tutorial that makes it clear what's involved in bitcoin mining, preferably in simple language?
Solving algorithms. It takes a really long time to show you a in depth explanation tutorial so I am pointing you to the youtube video series of mining. I am a firm believer that you learn much more when you are looking at the topic that you are interested being done in real time rather than reading tutorials, although I know this differs from person to person.
https://www.youtube.com/results?search_query=bitcoin+miningDon't give attention to the first video, all others are related to your question.