The Green Party candidate Ralph Nader (in)famously is part of the 2000 election because many people think that he siphoned votes from the Democrat candidate (Al Gore) which may have been a factor in Gore's defeat.
Here's a simplified view of what I mean. Let's say there are 100 people total. Now let's say the election is very close at 50 50. If any one person changes their vote, then the winner is decided. If a third party enters the race, then one of the original candidates will have their vote split. If Gore had 50 votes, but then lost say 20 of them to Nader, then he'll be left with 30 after all is said and done. Bush will still have 50 votes and this leads him to win the election.
Note: Gore won the popular vote, but lost the electoral college. The electoral college is the true deciding body that determines the president.
So based on the second paragraph, that's just one simplified example of how a third party effectively "spoils" the race. Of course, many could easily argue that a third party (or many more parties) is actually a good thing because it encourages many voices to join the political arena. Those advocates would say that having 2 parties leads to stagnation and lack of growth, not to mention lack of representation of everyone.
In short, many people think the third party candidate Ralph Nader redirected votes away from Al Gore which may have cost him the election. However, there may be other factors that contributed.