A blog post by David Perry (@KJ6CCZ) gives a thorough explanation of how mining works without any of the specific details that “might scare the non-techies”.  Excerpts:

Core concepts and terms:

• Hash:
  I tell you that I added two numbers together and the result was 14,862. Given only that number there’s no way you could tell me what two numbers I added to get that total, but it would be easy to reproduce my result if I asked you to add 3,608 and 11,254.
• Block:
  Transactions are bundled up into big chunks of data called blocks. These blocks are linked together in such a way that each one proves that the block before it was valid.
• Difficulty: 
  Ensure that [Bitcoin’s] math problems are hard enough that it always takes the combined efforts of all the miners around 10 minutes to solve a block.

The more miners there are, the higher the difficulty goes. The higher the difficulty goes, the harder it is to commit fraud on the Bitcoin network.

Sudden changes in the value of a bitcoin can make or break mining operations. Granted if a drop in price knocks some miners out of the picture, difficulty will decrease to accommodate, but that takes time. Miners follow the market - the market does not follow the miners.

Discussion about this blog post can be found on Hacker News.

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