Anyone paying close attention to the presidential race will have noticed that many Republican candidates are worried that Donald Trump may ultimately end up running not as a Republican, but as an Independent candidate. There's been a lot of speculation about this possibility over the last few months, with Trump himself saying that there's a chance he would leave the Republicans and run independently. Republican party members have not been quiet about their dislike of Trump, so seemingly getting rid of him from their party would be a godsend. They wouldn't have to deal with him in their debates or their polls, after all. So why would Trump running as an Independent be a problem for Republicans?
To put it briefly, if Trump ran as a third party candidate, it could completely obliterate the odds that either Republican or Trump (the only conservatives in the mix) would win the presidency. Presuming that Trump would continue to poll so well with conservatives, and that he would continue to do so as an Independent candidate, the Republican party would really have their work cut out for them convincing swing voters to go for their candidate instead of Trump in November 2016. They would also likely need to work to get unhappy Republicans to toe the party line instead of side with Trump, effectively needing to regain votes that the party would have in the bag without an Independent Trump in the mix.
The reason it shakes out this way is our two-party system, in which Republicans and Democrats are the only viable options in any major election. There are third parties, such as the Green Party and the Libertarian Party, but neither have ever won the White House, and it's rare that they get seats in Congress. With only two parties truly in play, voters who might agree more with a third party's platform and ideals are generally obliged to ultimately cast a vote for whichever of the major two parties they identify with the most, or to vote against the party they are the most opposed to.
So think about the Libertarian friend you made freshman year of college. He really hated both Republicans and Democrats, but since he was terrified of potentially having his phone records submitted to the NSA, he decided to vote Republican in the election, even though he really didn't like anything else about the Republican party and couldn't see a good reason to vote Democrat. There's no other party that stands a chance in a major election, so if we want to vote at all, we're obliged to vote for one of the two big parties if we want to support a candidate who has a chance of actually winning.
If Trump decides to run Independent, centrist and conservative voters who are disgruntled with both parties could see a vote for him as a way to stick it to both Democrats and Republicans, and as a chance to vote for a candidate whom they feel most closely represents their values. Because Trump is so far to the right ideologically, he is unlikely to steal any voters from the Democrats, but if he goes Independent, he will most likely take many of his current Republican-identifying supporters with him. Trump would take nothing from the left, but would potentially take a chunk of otherwise-Republican votes, as well as some swing votes that Republicans would hope to convert later in the election process.
This amounts to legitimate fears from the Republican party because losing a critical number of votes to Trump would almost certainly mean a win for the Democrats. The Democrats would more or less be sitting pretty while Trump secures enough votes to significantly lower the overall percentage of votes and electoral college points, making a Republican win virtually impossible. Meanwhile, Trump himself could likely never earn enough votes to overtake the percentage of Republican or Democrat votes. The likely scenario is a strong win for the Democrats, with the Republicans in a far second place (having lost so many voters to Trump), and Trump in an even further third place, with just enough votes from conservative voters to put him on the map.
The two-party voting system can be a little difficult to grasp, even though it seems like it would be straightforward, since we're given only two real parties to grapple with. This U.K.-based video from 2011 breaks down the two-party voting system that we have in the U.S., and it illustrates how a popular third party candidate can spell real trouble for competing major parties.
All of this puts the presidential race into new perspective. If Trump decides to abandon the Republicans and run as an Independent candidate, all conservatives will have a tough battle to fight getting a right-leaning candidate in office. This amounts to encouraging news to the Democrats, and extremely troublesome news for the Republican party.