In what way does the existence of minor parties also work to strengthen the united states two party system?

The two major parties occasionally have a platform or candidate that becomes lost or strays away from their party's fundamental beliefs. The importance of 3rd parties is that they serve as a wake-up call to the two parties, and force them to recognize emerging problems and/or constituencies. 

The two major parties sometimes become lost within their own constituencies. The importance of 3rd parties is that they serve as a wake-up call to the two parties, and force them to recognize emerging problems and/or constituencies. Once awakened, one or the other of the major parties tends to co-opt the issues of the 3rd party, thus killing it. This is why 3rd parties tend not to last or make a long term impact on American politics.