https://en.wikipedia.org/wiki/Cryptocurrency
 

So mining is the equivalent of a distributed computing check clearinghouse.

Ok, that was helpful.  A "block" is a batch of new cryptocurrency transactions which are of course, encrypted.  The miners are essentially attempting to break the encryption in order to verify the transactions.  If I understand, there are a bunch of miners working on any one block and the first one to break the encryption is rewarded with coin.  Seems like if they want someone to verify the contents of a block, they would give them the key, not make you break into it.  I think I have a little better understanding now but it still makes no sense to me.  Seems like an awful amount of effort built into something that they want you to do.

Just when I thought I had a better understanding, Haywire's last comment throws me in a conundrum!
 
"These equations are a product of the encryption designed to protect transaction data on the digital ledger."
 
So yes, a lot of effort to encrypt and protect transaction data... makes good sense.
 
Best,

HaywireHaywood
The miners are essentially attempting to break the encryption in order to verify the transactions.  If I understand, there are a bunch of miners working on any one block and the first one to break the encryption is rewarded with coin.

To be clear, the activity of mining does not break the private/public key pairs which secure each accout/"address". To be clearer, they aren't breaking encryption at all; they are using encryption. Figuring out the private key which secures the funds in each account/"address" is basically impossible.
The cryptography necessary to verify the ledger is quite simple. Mining is often, essentially, purposely created waste added on, automatically based on the size of the mining pool, based on the author's intended wishes for the design of the cryptocurrency, in order to prove that some sort of supposed work has been performed. Yes it does serve the purpose of ensuring that account balances are accurate and for eliminating fraud and theft at the mathematic level, but it also often has designed into it a certain amount of wasteful overhead to supposedly legitimize the currency and to slow growth and inflation to some degree.
Fraud and theft is essentially mathematically impossible in the cryptocurrency world, but it's security isn't very much thanks to the work of miners. It is still possible for fraud and theft to exist through social engineering and by people saving their public/private key pairs in improperly secured exchanges or services -- for convenience -- which then later steal funds, get hacked, or leak the public/private key pairs to criminals. The public key is the "address"/account, and the private key is necessary each time any amount of currency is transferred away from the address.

I take it back.  I have absolutely no clue what mining is or why it exists.  It just makes my head hurt.  Unsubscribing.  LOL

Ah, fantastic timing on this video release:

Eventually the hashing power will stabilize. Once the cost to produce starts to near value if coins, new mining operations will switch to other coins. Of course it's all theory and hasn't yet been tested. Certainly the availability of graphics cards now shows that the high growth phase is ending/ended. Long term, eventually the entirety of the bitcoins/ altcoins will be mined and the incentive switches to transaction fees for the reward.

Hoggle
What doesn’t make sense to me is how mess coins will be available over time while the computers needed for the encryption of the blocks will increase with time. It really seems like a bubble since we will hit a point in which it will take twice as long to make a profit as it does now and twice as many miners mining to support the coins already mined.

most coins have what is called a difficulty. this sets how hard it will be to find a new block such that on AVG a new block will be minted every X minutes, for BTC its 10. so as Computational power increases the difficulty will increase such that blocks will continue to be minted at the same rate, not longer or shorter timeframes. so no matter how much computational power, or how little, you throw at the coin there is always a stable output of new coins for miners.
 
so no you will not need constantly increasing massive amounts of computational power to support previous coins. you could secure it with just a single 1 core atom processor and continue a blockchain minting a new block every ~10 minutes after the difficulty adjusts. but because of the 51% attack the more power you have on the blockchain the more secure it is.