Whomever solves it get's a reward + whatever transaction fees happened since the last solution. That reward was initially 50 BTC, it has halved 4 times now, 50,25,12.5, now 6.25.
Something like a lottery that gets drawn every ten minutes, but instead of somebody rewarding you, you just have to show the network that you found the solution.
After the halving, the reward per round is... well cut in half.
This affects mining profitability. Puts lots of hardware in locations at negative profitability so they'll have to shut down and buy new hardware, find cheaper electricity, etc.
Whatever happens, difficulty will be adjusted so the same 10ish minute block reward time is maintained.
What does this do to value? Eh, the bitcoin market isn't very rational or consistent. Miners will have less to sell, certainly, but people will have all sorts of ideas of what it will do to the price of bitcoin and since so much of bitcoin is speculation and so little is using it for any real transactional purpose, who knows?
