Luca's meaningless thoughts  

Bitcoin is one of the most subversive ideas I ever read, it's as scary as exciting in how it could change the world economy dynamics if it works.

Bitcoin is (quoting WeUseCoins.com):

Decentralized

Bitcoin is the first digital currency that is completely distributed. The network is made up of users like yourself so no bank or payment processor is required between you and whoever you're trading with. This decentralization is the basis for Bitcoin's security and freedom.

Worldwide

Your Bitcoins can be accessed from anywhere with an Internet connection. Anybody can start mining, buying, selling or accepting Bitcoins regardless of their location.

No small print

If you have Bitcoins, you can send them to anyone else with a Bitcoin address. There are no limits, no special rules to follow or forms to fill out.

More complex types of transactions can be built on top of Bitcoin as well, but sometimes you just want to send money from A to B without worrying about limits and policies.

Very low fees

Currently you can send Bitcoin transactions for free. However, a fee on the order of 1 bitcent will eventually be necessary for your transaction to be processed more quickly. Miners compete on fees, which ensures that they will always stay low in the long run. More on transaction fees (Bitcoin Wiki).

Own your money!

You don't have to be a criminal to wake up one day and find your account has been frozen. Rules vary from place to place, but in most jurisdictions accounts may be frozen by credit card collection agencies, by a spouse filing for divorce, by mistake or for terms of service violations.

In contrast, Bitcoins are like cash - seizing them requires access to your private keys, which could be placed on a USB stick, thereby enjoying the full legal and practical protections of physical property.

Here is a video, if you are too lazy to read:

If you want some more detailed information, there is a paper describing the technical side of the project (which I read and didn't fully understand, to be honest).

You have to add bitcoin mining to the equation. Which is not very well explained there. Bitcoin mining is a business, just like gold mining is. You need resources to do it, and if you don't do it efficiently, you'll loose money (the electricity and hardware cost will supersede what you're earning).

Quoting again:

The mining difficulty expresses how much harder the current block is to generate compared to the first block. So a difficulty of 70000 means to generate the current block you have to do 70000 times more work than Satoshi had to do generating the first block. Though be fair though, back then mining was a lot slower and less optimized.

The difficulty changes every 2016 blocks. The network tries to change it such that 2016 blocks at the current global network processing power take about 14 days. That's why, when the network power rises, the difficulty rises as well.