What was significant about the transfer of power between parties in 1801?

The main significance regarding the transfer of power between parties in 1801 is that this was the first time in American politics where a two-party system had formed, which had wide implications that are still relevant today. 

In reference, The Encyclopædia Britannica defines "political machine" as, "in U.S. politics, a party organization, headed by a single boss or small autocratic group, that commands enough votes to maintain political and administrative control of a city, county, or state".

SO: It's purpose primarily serves to gain and maintain political and administrative control of city/county/state, none the less the population.