Just to give some specifics in addition to David Grayson's answer:

At current difficulty levels, mining a block requires computing an average of

29,973,900,941,385,007,104

hash operations. An ordinary computer can perform perhaps 10,000,000 such operations per second. At that rate, such a computer would take about 95,046 years to mine one block, on average. If the computer draws 100 watts of electricity, it would use 3,469,201 kilowatt-hours of electricity over that time. Electrity prices are somewhere around US $0.10 per kWh, so that would cost US $346,920 in electricity alone - much more than the $12,325 of the block reward.

For obvious reasons, most miners today don't use ordinary computers, but rather specialized ASIC hardware that is considerably more efficient (and more expensive) than an ordinary computer.

It is a lot of work and it requires a lot of computing power. To get the 25 BTC reward for a block (also known as the coinbase reward), you have to create the block in the first place. It is difficult to create blocks. A valid block will have to meet a large number of conditions, including that its header has a 256-bit hash whose numerical value is under a certain target. The target generally gets lower (more difficult) over time as more people try to create blocks.

Since the hash function is hard to reverse, you basically have to brute force it, trying many different possible variations on the data in the block and computing the hash of each one, until you find a block whose hash is low enough. If you are lucky, you will find such a block. Then you would broadcast that block to the world, and since you created the block it will contain a transaction giving the coinbase reward to your own address. This process of calculating hashes and making new blocks is called mining and it is almost impossible to make money doing it yourself these days, so you would have to join a mining pool.

A miner confirms transactions by creating a block and including transactions in them. The new block contains a hash of the previous block, so it also serves as an extra confirmation for all the previous blocks in the chain and all the transactions in them.

Besides confirming the transactions in the block (which prevents the corresponding funds from being double-spent) the new block also adds to the security of all previous blocks since altering any block in the chain requires altering it and all subsequent blocks.

In my mind that it what justifies the reward.