What *is* mining?

[jongameson]

What are blocks?  What are shares?  And what is the "best share" value in cgminer?  How is this number derived?  And how does this relate to difficulty??  How is an address chosen to receive the reward?

What causes some shares to become Accepted, and some Rejected?

Which part of mining involves transaction processing?  Or does this only happen some of the time?  What does it do the rest of the time, when it is not busy?

These are valid questions EVERY newbie has probably asked themselves at some point in time.  And some of us don't know the answers, like me    

[odolvlobo]

http://lmgtfy.com/?q=what+is+bitcoin+mining&l=1

Maybe that's too basic. Here are your answers:

Transactions are added to the block chain a block at a time.
When mining in a pool, a successful hash earns you a share of the next block reward that the pool receives. The difficulty is lower, so many hashes are successful even though they don't solve a block.
Best share is the one with the lowest hash converted to a difficulty value.
You give the mining software the address to receive the reward.
Shares that qualify are accepted. Hashes that are out-of-date or invalid are rejected.
Mining is all about transaction processing and nothing else.

[jongameson]

I know the whole deal is "solving math problems" so I just liken it to solving crossword puzzles or sudoku when explaning it to my mom 

[odolvlobo]

I know the whole deal is "solving math problems" so I just liken it to solving crossword puzzles or sudoku when explaning it to my mom  

The "solving hard math problems" explanation is a stupid analogy. A better analogy is picking lottery numbers, but even that is not really the point. The point of mining is validating transactions.

[Mach]

The part I am still trying to figure out is how do transactions get processed after all bitcoins are mined?  Since transactions are only attached to a valid bitcoin block and there are a finite number of bitcoins that will ever be produced, will we lose the ability to perform transactions once all bitcoins have been mined?

[kuverty]

I know the whole deal is "solving math problems" so I just liken it to solving crossword puzzles or sudoku when explaning it to my mom  

The "solving hard math problems" explanation is a stupid analogy. A better analogy is picking lottery numbers, but even that is not really the point. The point of mining is validating transactions.

Yeah. As a math student, I find that annoying. It's just poo-loads of the most trivial kind of computations.

The part I am still trying to figure out is how do transactions get processed after all bitcoins are mined?  Since transactions are only attached to a valid bitcoin block and there are a finite number of bitcoins that will ever be produced, will we lose the ability to perform transactions once all bitcoins have been mined?

Miners will keep mining blocks, there as just no longer any block rewards. The miners now get their income from the transaction fees, so there is still incentive for mining. You can do mining, just keep hashing blocks, there does not need to be a BTC reward for every new block.

[infinitybo]

To get back to the point blocks are chained in the sense of having the ID of the previous block in its header and such.