There are two main science goals for the Cassini death dive into Saturn that I know of. One of them is simply higher scale imagery of objects closer to Saturn as it journeys inwards. The other is that it will fly between the planet and the rings, and based upon the radio signals coming back to Earth, we should be able to, for the first time, directly measure the mass of the rings to within around 1019 kg. This may seem pretty coarse, but there are several specific prediction papers (including one of mine ...) that estimates the ring mass in multiples of the moon Mimas, which has a mass of $3.8\cdot 10^{19}$ kg.
A third that I thought of a few hours after writing this is that the spectrometers on board should be able to sample the saturnian atmosphere during entry and send back detailed composition information, just as it did when flying through the plumes of Enceladus.