A faithless elector is an elector that, within the United States Electoral College, does not vote for the presidential candidate whom won the state in which the elector is serving. Instead, the elector either casts his or her vote for another person who is not in the presidential race, or decides not to cast a vote at all.
There are many reasons why an elector may choose to cast their single vote for another person or to opt out of voting. Many electors choose to vote for someone else merely because they are concerned with the capabilities of the candidate that their state voted to elect. In a recent example, four electors to the 2016 Electoral College opted to vote for separate individuals, rather than for Hillary Clinton, although she won the states of Washington and Hawaii.
A faithless elector, in recent times, has never affected the outcome of a presidential election. They are also very rare: most electors have a high status within his/her chosen political party, and would be subject to party discipline if s/he did not vote for the chosen candidate.