Some voters with Libertarian leanings choose not to vote Libertarian because they don't want to throw their votes away. Voting for the Libertarian candidate for president, however, doesn't waste your vote. Doing so multiplies the power of your vote by 10.
For a Democrat or a Republican to run a successful presidential race, they need to win 50% of the vote (with a few notable exceptions). For a Libertarian to run a successful presidential race, they only need to win 5% of the vote. That's enough for the party to get federal backing on their next race and for them to get their message to voters.
Would the Libertarians getting 5% of the presidential vote be relevant? Considering how close the Republicans and Democrats get to each other (in an attempt to win votes from middle-of-the-road voters), a bigger national presence for the Libertarians would make as big a difference for national policy as the difference between a Democrat winning the White House and a Republican doing so.
For nonpresidential elections, there's no magic 5% number, but the Libertarians still need fewer votes than the Republicans or Democrats. The Libertarians don't need to win the race; they just need to take enough votes that the Republicans and Democrats have to adjust their policies to win some of those votes back.
One advantage that Libertarians have as a third party is that they stand to take votes from both the socially liberal Democrats and fiscally conservative Republicans. Unlike the Greens, the Libertarians can garner votes without tipping the balance too much toward either the Democrats or Republicans. Those who'd otherwise vote Democrat or Republican don't have to worry about inadvertently helping one party or the other.
Of course, while the US political scene would be richer and more mature with a Libertarian voice within it, you wouldn't want them actually to win an election.