For digital cash system, a payment network necessarily should have valid accounts, balances and transaction records. The biggest bottleneck common to every payment network is the double spending problem which is the case when same money is used multiple times to do transactions.
To prevent double spending, all transactions have to be recorded and validated every time in a central server where all the balance records are kept. However, in a decentralized network, every node on the network has to do the job of a server; it has to maintain list of transactions and balance records. Thus, it is compulsory for all nodes/entities in the network to keep a consensus about all these records. This was achieved by using the blockchain technology in bitcoins.
So we can say that bitcoins like other cryptocurrencies are mere token entries stored in the decentralized databases that keep consensus of all balance and account records. It is to be noted that cryptography is used extensively to secure the consensus records. Bitcoins and other cryptocurrencies are secured by math and logic more than anything else.
Bitcoins and cyptocurrencies have gained recognition and adoption based on their perceived value by their creators and users.
Bitcoin works on the same concept, the more people participate; the more value is created.