Bitcoin is a virtual currency that is using a p2p network model to process all the transactions without any central node or authority. It is run by the network for the users. People put together their computational resources and they are used to run the network.
Part of the security relies on solving a difficult computational task each time when the network accepts a new batch of transactions.
I don’t have anything really new to add over what is available on Wikipedia or in other posts. I’m keeping this just as a note to myself to keep track of my effort: I’ve read a couple of papers from here, but I still need to open the most recent ones.