In a way what happened in Europe in the Modern era already justifies the quote by Castro.
Let's recall that towards the end of the feudal era it was the landed aristocracy that held the power, and it was the rising bourgeoisie that challenged that power; the former were exploitative and the latter were exploited. The revolutions through Europe upset and then altered that balance of power with the bourgeoisie eventually holding the dominant position and the aristocracy coming to some kind of accommodation. The details of which varied with nation.
And these were called revolutions: the English revolution, the French revolution etc.
Of course Fidel was talking in a Marxist perspective - but the same general principle holds.
In Communism & Democracy, Mike Makin-Waite described how the International Communist movement going on from its beginning in the European Enlightment, and then further inspired by Marx, split in the wake of WWI and the Bolshevik revolution on the question of how politically, the emancipation from 'wage-slavery' was to be achieved.
Two hostile camps formed. One side argued for reform, this would be exemplified by the Social Democrats in Europe; the other side argued for an armed insurrection, that is revolution. This was the side argued by Lenin, and exemplified by Russia during the October Revolution of 1917. Lenin quotes Marx in his book The State and Revolution:
Between Capitalist and Communist society lies the period of revolutionary transformation of one into the other. Corresponding to this is a political transition period in which the state can be nothing but the revolutionary dictatorship of the proletariat.
An analogy here would be the emancipation of the black african slaves in the North America. Their emancipation was not achieved peacefully, but through violence - the American Civil War - or one might say, the American Revolution. The difference here of course, is that they had a professional standing army, and the war was of two polities, rather than a class war.
In the theory of revolution outlined by Lenin, a change in the real political conditions of a polity would need to go through a period of 'dictatorship'; this would be temporary in order to establish the political consensus. It's required because a new governing authority had to exert its authority before it's authority is accepted - hence 'dictatorship'. It shouldn't be confused with a dictatorship like that of Mussolinis fascism.
The term and the concept of 'the dictatorship of the proletariat' did not originate with either Marx or Lenin but by a Joseph Wedermeyer, a Prussian military officer; which may go some way in explaining it's unfortunate name given the associations the term dictatorship today.
Dictatorship is not the end, by which I mean the aim of a Communist revolution; the aim of Communism as in traditional Liberalism is freedom. It's probably worth remarking that in the same work Lenin admitted that liberal democracy was probably the best form of government that could be achieved before communism.