That is a bit of a metaphor. The concept of "a bitcoin" is really an abstraction that allows us to converse a bit more easily about using the results of the bitcoin protocol as a currency.  In actuality no "bitcoins" actually exist or ever will.  What exists is a public ledger and a protocol with rules about what requirements must be met to update the ledger.  Miners follow these rules to add transactions to the ledger and the entire network ensures that the miners are following the proper rules.  In exchange the entire network allows each new ledger entry to include a special transaction having no input that assigns outputs to one or more addresses, but does not exceed a value specified by the protocol.