Change
Introduction
When a UTXO is spent, it must be consumed entirely. If the value of the UTXO is greater than the amount being spent, then the difference in the amount must be allocated to a new address that the spender owns; this is a change address.
Typical example
In a standard payment scenario, the sender consumes a single UTXO, paying the spending amount to the receiver's address, then receiving the change into a new address that they control to take advantage of privacy.
In this example, we can see that address 197vdcD73wQF5FviYXXgv6cXJBibc9phdq held a UTXO containing 47,097 Satoshis.
They paid 10,000 Satoshis to 1C7UVhVnspkxot82j6ooMxUUFEWy4Pj1tc and received 36,871 Satoshis as change into address 1LNq2ZePCj2mycctrvQqBVnTLeaJeyDeR4.
The difference of 226 Satoshis was paid as Transaction fees to the miner who found block 605,046.
Change back to spending address
In a naive implementation, the sender consumes a single UTXO as in the previous example, with the only difference being to receive the change into the same spending address. This means of transacting is not recommended as it does not take advantage of Bitcoin's privacy model.
This example also demonstrates where the difference between the input and output is only the mining fee since a message is being written to the blockchain.
Consolidating UTXOs
In some cases, the spender may have many UTXOs that they would like to consolidate. This has the added benefit of reducing the network's total UTXO set, shrinking the database that all nodes maintain. Consequently, the computation for processing these inputs could be expensive. Miners could potentially process these types of transactions at a lower fee.
An example can be found here.