Full Idea
In a proper demonstrative argument, the middle term must be explanatory of the conclusion, in a very specific sense: the middle term must state what properly belongs to the definition of the kind of phenomenon in question.
Clarification
The 'middle term' is the transitional term in a syllogism
Gist of Idea
In a demonstration the middle term explains, by being part of the definition
Source
Kathrin Koslicki (Essence, Necessity and Explanation [2012], 13.3.1)
Book Reference
'Contemporary Aristotelian Metaphysics', ed/tr. Tahko,Tuomas [CUP 2012], p.199
A Reaction
So 'All men are mortal, S is a man, so S is mortal'. The middle term is 'man', which gives a generic explanation for why S is mortal. Explanation as categorisation? I don't think this is the whole story of Aristotelian explanation.