What on earth is a Subresultant?

I am investigating polynomial roots, for example a quartic can have several root configurations (1,1,1,1),(2,1,1),(2,2),(3,1),(4)

I have used resultants and determinants to study when we get repeated roots, but for example in the (2,2) case when there are 2 repeated roots it is a bit more complicated, I was pointed in the direction of thinking about subresultants, but I can't even find a definition of a subresultant anywhere! Mathematica can calculate them, but MathWorld doesn't explain what a subresultant actually is. Does anyone know?

Thanks