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

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.

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.