A blockchain consists of data blocks which contain all transactions of the network. The creation of those blocks is called mining. This process gets performed by the so called miners. Everybody can, at least in theory, become a miner if he has energy, internet, hardware, software and the necessary knowledge.
Miner are constantly in competition with each other about who can solve the task that the algorithm of the blockchain has defined. As soon as a miner has found the solution to the task all other miner have to confirm it. If the solution was correct he gets paid the block-rewards. The block-reward consists of newly created coins and the transaction fees.
The blockchain is stored on nodes and full nodes that own a copy of the blockchain. For this reason the data is always available in the form that the majority of the network has agreed on.