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Definitely poverty, and the search for an easy scapegoat.
Plus the fact that Germany was quite conservative at the time, and was yearning for the old monarchic order, with an emperor at the top, so this leader figure was quite attractive.
Then of course there was this hatred against the countries of the Entente for giving germany the sole blame for WW1, having to pay massive reparations, and being banned to amass a military.

When a country is in disorder, fascism can appear as the ideal solution. As @ragingloli already said, Germany was in a bad situation after WW1 and Adolf Hitler appeared as a strong leader who could get them out of the crisis and give them back their pride as a country. Adolf Hitler was inspired by the old Greeks and their ideal human being, see this German sculpture: http://www.chgs.umn.edu/images/sculpt_b ... rmacht.jpg. It shows the strong, arian figure that Hitler was obsessed with.
This is my guess, but I don’t claim any knowledge.

As the others have said, this isn’t a simple question – each fascist regime over the last couple of hundred years has been a little different.
But there are two essential pieces for any fascistic government. The details vary, but two essentials:
1) A powerful leader. Charisma helps, too. The person doesn’t need to be intelligent (Hitler) or strategic or even particularly conniving. The person just needs to be a leader in the sense that he can get people to do what he says. If there is a philosophy (religious or otherwise) it lends legitimacy (or at least rationale) to what he is doing, but that’s not essential. The key point is that there’s a leader who is the focal point.
2) A docile, non-questioning population – this is why Hitler, among others, was so successful. If Germany hadn’t been so worn out from losing WWI and the subsequent depression in Germany, they might have been less docile and less willing to follow Hitler. Same with Italy and Mussolini. And same in a number of states in Africa, although there the issue is not losing WWI or WW2, but being docile because of poverty and low standards of living.
Again, each instance of fascism has its own peculiarities, but the two elements above are essential.