Balances in the bitcoin system are tracked by chains (actually trees) of linked transactions, starting with an original ``coinbase'' transaction which grants coins from nowhere to miners as a reward for securing the network.
There is nowhere that coins themselves are stored; there are only trees which may be extended at the leaves. Each leaf node (called a utxo internally) has a value associated to it. Your ``balance'' is the sum of all leaf nodes which you have authority to extend from.