I would paraphrase "rash humour" as irascible temper or fickle temper. Based on what Brutus said earlier, Cassius does not so much have a persisting angry mood; his character is better described as choleric (emphasis mine):
O Cassius, you are yoked with a lamb
That carries anger as the flint bears fire;
Who, much enforced, shows a hasty spark,
And straight is cold again.
Shakespeare's main source for Julius Caesar is Plutarch's "Life of Brutus" (from the Parallel Lives as translated by Thomas North. Here's the relevant description of Cassius in The Life of Marcus Brutus:
And as for Cassius, a hot, choleric, and cruel man, that would oftentimes be carried away from justice for gain, it was certainly thought that he made war and put himself into sundry dangers, more to have absolute power and authority than to defend the liberty of his country.
Plutarch does not mention Cassius's mother, so it appears that Shakespeare made up the claim that Cassius inherited his irascible temper from her. It is less clear why Shakespeare would add this sort of detail. However, Brutus goes on to say,
(...) from henceforth,
When you are over-earnest with your Brutus,
He'll think your mother chides, and leave you so.
Possibly, the two men use Cassius's mother as a figurative lightning rod, i.e. as a means of diverting blame for Cassius's irascibility to someone else, in order to make their own working relationship less vulnerable to Cassius's temper.
Update: Rand al'Thor wrote in a comment:
I can't find a good source, but I think it's a standard expression in English (especially older English such as Shakespeare's) to say that an attribute was given you by your mother just meaning you had it from birth.
My paraphrase as "inherited" is based on two editions of Julius Caesar: one by Norman Sanders (New Penguin Shakespeare) and one by T. S. Dorsch (Aden Shakespeare, 1965, reprinted 1983). Both editors use the term "inherited". Note that in this context, it is difficult to claim that Cassius did not get his irascible temper from his mother (i.e. that it is a trait he was born with without his mother having anything to do with it), due to Brutus's answer.