Such a term is a 'big term' not in length but in the size of the speaker's social status or educational level. The language of your passage has a distinctly ironic sense, albeit the irony is rather American in tone, and so I would assume that the speaker is in the position of teacher talking to a group of students considered dumb by society; they expect to be patronised, so she parodies the stereotypes they expect from her by pretending to reassure them that even they can understand an 'educated' word/concept like 'syllogism'.
Similarly, the speaker is dismissing the difficulty of understanding mathematical logic, which has 'big' terms like 'syllogism' or 'predicate', by using a term that resonates with his/her listeners. They will have likely dismissed their younger siblings, learning new skills, with the contemptuous "Can't you even do that simple stuff?" 'Stuff' is just a generic term, usually dismissive, meaning 'whatever it is/was', etc. For example: Q:"What did you do last week?", A:"Oh, just stuff." This is intended to make them contemplate that logic is just like making a tidy hayrick, in that we all start as novices, and by hard endeavour we eventually reach the stage of describing our skill as nothing more than 'simple stuff'.