Bitcoins are based on the blockchain technology. A blockchain is a distributed ledger that is synchronised between multiple computers. These computers, or nodes, together maintain the Bitcoin network. The nodes contribute the hardware and electricity which the blockchain needs to operate and are themselves paid for it with Bitcoins. This process, called mining, provides incentive to its participants and ensures that the blockchain continues, even if a single node leaves the network.
Bitcoin is a so-called crypto currency. A better word is crypto asset since actually it is so far not clear if it is a currency.