What is an unspent transaction output (UTXO)?

A Bitcoin wallet contains a collection of unspent transaction outputs (UTXO), at least one for each transaction that you have received. The sum of the UTXOs controlled by your wallet is your wallet balance. 

Similar to physical cash, a UTXO is not divisible.
For example, if a wallet contains 0.5 BTC and the owner wants to send 0.4 BTC to a friend, the resulting transaction will create two UTXOs consisting of the whole 0.5 BTC:

(1) The 0.4 BTC is sent to the friend's receiving Bitcoin address
(2) The remaining 0.1 BTC is sent back to the owner's wallet to be spent in future transactions, also called a "change output"

Note: For simplicity sake the network fees were not included in this example.