A singular element of truth or wisdom within a greater story, narrative, speech, or claim, especially when most or all other elements are fictitious or of questionable veracity. I think the governor's speech is a bunch of hogwash by and large, but there is a kernel of truth in what he said about the need for lower taxes.
Prov. You have to work if you want to get anything good. If you want to be a good pianist, you have to practice every day. He that would eat the kernel must crack the nut.