I'll give it a try:

You can think of hashing as a 'mathematical equation' where you produce a (random) output depending on the input.
Now, when you mine, you are basically calculating hashes (with the TX's as input) until you have found a hash with X leading 0's.
How much 0's are needed is defined by the difficulty of the network. This difficulty adjusts every 2 weeks to get a 6 blocks per hour 'speed'.
Each time you mine a block the first transaction in this block is the coinbase transaction (has nothing to do with coinbase.com).
This coinbase transaction contains the freshly mined BTC's to the miners address.

Basically its a probability game. The miner with the highest hashrate (most calculations per second) has the highest chance of mining a block (calculating a valid hash) proportionally.


Thats just a very basic description of the mining process. Feel free to ask more detailed questions.