Keeping to basics (there's much more to be said, if you feel this is too lmited). Fascism is the name of a political movement created in 1919, around a platform of nationalism, former interventionism and veteran movements (most notable that of the arditi) that touched on social issues, mostly inherited by the short lived Futurist Party.

Its name - or rather the extended name of Fasci di Combattimento (fasci of the combatants) - tied back to an established tradition and to the recent experience of the war.

While the fasces, as a symbol, date back to the public authority in the Roman Republic (and had therefore been used in France and the US), in Italy, at least in the beginning, the reference was less academic and more down to earth: a fascio is a sheaf of sticks, a traditional image to imply strength out of unity of equals. It was routinely used by political formations, as it was alternative and more neutral to the socialist "leagues" i.e. the agrarian unions. In those years we had a "democratic fascio", various interventionist fasci appeared before and during the Great War, most notable the Fascio Parlamentare di Difesa Nazionale (the core nationalist-interventionist political block after Caporetto); but the word also tied back to the Sicilian Fasci of 1894-96 whose revolt had been one of the first "socialist" uprisings of unified Italy.

As you can see a fairly generic term, analogous to league, union, party, etc.

After the foundation of the Milanese Fascio, under the good officies of Mussolini, other Fasci appeared in different cities - often merging with the pre-ezisting futurist or arditi associations. The movement, at first dramatically unsuccesful, found new strength with the support of the land owners of the Po valley.

In 1921 Mussolini, now the political leader of the "movement" transitioned it into a Party (Partito Nazionale Fascista) with a more conservative program that included liberal openings. After his appoinment as Prime Minister in 1922 large chunks of the political establishment as well as the public flocked to the PNF that soon rose to the dominant political party.

In 1926 this state of things was sanctioned by the abolition of the other parties - in fact reduced by then to empty shells. This took place in the context of the so called leggi fascistissime or "most fascist laws".

The plebiscite of 1929 is generally regarded as the definitive moment of establishment of the Fascist Regime, and of course in 1936 Italy would celebrate the creation of a Fascist Empire.

No matter what the word fascist seems to suggest to us. Fascism was to fascists a point of absolute pride and the regime propaganda attempted to frame it as an alternative (a third way) to both Communism and Democracies (later the US and UK would gain in the internal propaganda the less flattering definition of "plutocracies" - which, if you are unfamiliar with the term means essentially "power of the wealth"). The most various things became fascist things, from sportive triumphs to marches and parades to physical education. As gerarca Giuseppe Bottai explained within the State one saw the realization of the highest moral values of their life and thus moved beyond everything within them that was partial: personal gain, interest, life itself if needed. Within the State one could see displayed in act the highest spiritual values: continuity beyond [the limitations of] time, moral greatness, enlightening mission for oneself and for others: therefore [the fascists] said … that the State was the ideal synthesis of material and immaterial values of one's ancestry and was the concrete form of the past and present generations. Thus the State, the Fascist State that is, was everything: the organism that served as summary and collection of all individualities. Nothing meaningful existed outside of Fascism: nothing outside of the Regime, everything within the Regime and for the Regime; discussion and critical thinking could exist only within the Regime, within boundaries, within Fascism, not against Fascism, within the Party, not against the Party, within the Fascist State, not against the Fascist State.

Our use of fascism - our contemporary use I'd say - is not really a product of a proper understanding of fascism (yes, fascism was still bad), nor would it necessarily mirror actual fascism, or even the way it was used in the immediate post war context. It appears to derive significantly from a few seminal works of fiction (I'd cast my lot here on 1984 being the most accurate to the spirit of fascism, despite being often reduced to its external apparatus rather than its internal purpose).

I have noted though that this use is significantly different in post-fascist nations, than it is in the "english world". The use of the term "fascist" from post war to now would be an interesting subject, that I fear I can't say much about, as I'd like to know more myself.

Germans would of course identify as National Socialist, but to which extent they used the broader definition of "fascism" I really can't say.