Let’s confront reality- your one individual vote will often not change the outcome of an election. Most congressional and state legislative districts are gerrymandered, so we know which party will win an election before it ever happens (unless you were in Massachusetts for Scott Brown’s upset). In addition, if an election is close enough to make each individual vote count, you simply move into the recount stage (which puts its primary emphasis on which votes are deemed valid).
However, individual votes do matter for minor parties and Independent candidates. The simplest function of this is the protest vote- you are an average citizen who is pissed off with the major party candidates, and you want to scream your displeasure by ‘spoiling’ your vote. This does serve a certain purpose, as it can force the major parties to expand their political base to account for your interests (provided enough similarly-minded voters also ‘protest vote’).
Nevertheless, there is a more practical function performed when you vote third party. Candidates outside of the major parties have difficulty creating a political base with the requisite fundraising capabilities and volunteer network. However, a strong showing at the polls can help alleviate this burden. For starters, many states have vote tests that determine ballot access for minor parties. Without meeting a certain polling threshold in previous elections, minor parties like the Libertarians and Greens must funnel thousands upon thousands of dollars to petition their way onto the ballot. However, if a party meets a vote test it can save this money for actual campaigning. In addition, strong electoral performances signal viability to potential donors and volunteers in subsequent bids for office for third party candidates. Thus, in a paradoxical fashion voting for a candidate who will not win can have a bigger effect than voting for the candidates that can.