Why should people work at all if they can run an algorithm that creates money?

Computer can't generate money. There always will be only fixed amount of Bitcoins, speaking mathematically - there's 13,000,000 Bitcoins right now, 20,000,000 absolutely precisely will be in 2025. It means that from 2014 to 2025 there will be emission of exact 7 million of Bitcoins. After that from 2025 to 2140 there will be only 280 bitcoins paid daily (compare with 3600 bitcoins daily paid today)

Satoshi Nakamoto/or group behind him could easily make all Bitcoins to be mined for 100 years slowly, very slowly, but I think he predicted that 10-15 years of slow emission is enough - it is not even slow - 15 years for emission of such huge currency is pretty huge.

For PR I wish Satoshi Nakamoto don't reward miners after 2014, because new users very often start their introduction to Bitcoin from mining - and for most people mining sounds like free Bitcoins, while its not free Bitcoins - the whole Bitcoin protocol designed the way to have restricted amount of money.

You can consider restricted nature of Bitcoin as blessing, nature shows the same pattern: we have only 1 earth, and lands is restricted and also being sold. Bitcoin is easily compared with lands, because purchasing 1 BTC today is the same like purchasing the whole New York territory 200 years ago. But funny thing about Bitcoin - you won't have to wait 200 years - the Bitcoin users will settle in that lands within next 5-10(maximum) years. They're already settling. The less users, more land, more users the less land.

Mining is the process which is like discovering new lands - you can discover only those lands where is no ocean, and every day ocean dry by opening 3600 miles of the land to be explored. And since there's too much miners - there's an army who's claiming their rights for the lands immediately after discovery. Then they sell this lands to the average users, who's just starting to dwell on that lands, but they have very poor means - they can't yet build the houses on that land, they still have only houses from woods and they are not appreciating their lands either.

Guess what happens after emission is done in 2025 (I don't count last million of Bitcoins emission, because it is very small amounts of reward for miners).

Miners is like a football teams, who's constantly playing on the field. But not like the regular football, because there is thousands of teams and even more football players participating in teams (team = mining pool, miner = football player).
Why do you need someone to play football in such serious activities like money? Because winning team usually has political weight in the program algorithm.
Why so complicated? In fact because you're trying to understand the deep thing about how Bitcoin works. But you don't need to know the word "miner" to use the system, because all of it is a background job done by software. Miners usually don't spend their personal time adjusting mining algorithms either - they just purchase hardware, plug it in, and enjoy the flight of hashrate/team play which computers play together to get supremacy right for the next block ;)

What is the blocks:
Imagine the blocks like train wagons: each wagon is checks, and checks pepresent the information written like this: "Alice wants to send Bob 1.34 BTC [+signature]". Miners can't get inside wagon or touch/change this messages, because there is unbreakable cryptographical lock. But miners have more important role for these wagon - they compete among each other to have right to perform some ceremony which puts the hash-seals on these wagons, confirming that this wagon goes after the wagon #316665 (previous block can be seen on http://blockchain.info - site that counts blocks publicly available for everyone and updated in a real time manner).

Each wagon (it is called block) is sent by the next miner who wins the global race. But where from this miner can get all of these checks which he must put into wagon? These checks before they get into wagon (block) they are collected at railway platform (in mempool = unconfirmed transactions list).

Who sends the checks to railway platform? This process is organized this way: users send checks to each other, they accumulate the checks in their own mempools first (even the clients participate in the process), these checks are accumulated in a file that is currently don't even prevail 1 megabyte per 10 minute (because there is usually averagely made only 500 transactions made by users around the world - look blockchain.info - there is a number of transactions included into each block - this is overall transactions that happened on the network)

After these checks laying on railway platform (mempool) are put into new wagon, it will be sealed by winning miner, then these wagon will be attached to the next wagon (again attachment is done cryptographically - the way you can't unnattach - because each wagon=block has a hash inside the seal representing the numeric order - one wagon after the other)