Full Idea
According the Lewis, the kernel of truth in truth-making is the idea that propositions have a subject matter. They are about things, so whether they are true or false depends on how those things stand.
Gist of Idea
The main idea of truth-making is that what a proposition is about is what matters
Source
Fraser MacBride (Truthmakers [2013], 2.4.1)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.20
A Reaction
[Lewis 'Things Qua Truth-makers' 2003] That sounds like the first step in the story, rather than the 'kernel' of the truth-making approach.