Change
Introduction
When the output of a transaction is used as the input of another transaction, the output must be spent in its entirety. The coin value of the output may be higher than what the user wishes to pay. In this case, the client generates a new Bitcoin address that spender owns, and sends the difference back to this address. This is known as change.
For example if a customer would like to buy a candy bar from a store for $1 but they only have a $20 bill. The customer cannot pay a partial denomination of the $20 bill; they must pay with the full bill and the merchant must give the customer change back. The merchant owes the customer $19 in this case. Bitcoin works in this same manner.
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.
An example of this type of transaction can be viewed here.
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.
An example of this is here.
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 UTXOs, thus shrinking the database that all nodes must maintain. On the other hand the computation for processing these inputs could be high. Potentially miners could process these types of transactions at a lower rate.
An example can be found here.