Fascism derives it's name from Latin word fasces. The fasces, which consisted of a bundle of rods that were tied around an axe, was an ancient Roman symbol of the authority of the civic magistrate. The symbolism of the fasces suggested strength through unity: a single rod is easily broken, while the bundle is difficult to break.
As such, Fascism rejects and resists autonomy of cultural or ethnic groups who are not considered part of the fascists' nation and who refuse to assimilate or are unable to be assimilated. Fascist are strong nationalists, and resists outside influences that would weaken the national identity, i.e. illegal immigration, foreign religions, outside cultural influences, etc. As such, this is identified with the Right in the US, which promotes Christianity, national sovereignty, and the stoppage of illegal immigration, whereas the left takes the opposite tact.
However, there is some consensus on socialism, which is the term the Nazis used. Fascism was originally linked to Mussolini, and not the Nazis.