Well, up to this point, it's mostly engineering. The science part will come when it starts showing what it finds around itself and unleashes the mass spectrometer - then we'll start to understand what the dirt/rocks/dust is made of.
The current theory is that Gale crater is a very old crater that was water-filled at some point of the planet's history, and different levels along the central peak (5 km high) appear to show records of different minerals - which scientists think may have been due to the change in the waters filling the crater. Midpoint, the mineral content seems to contain carbonates, which can precipitate out of an alkaline/neutral solution, whereas lower on the crater the minerals seems to contain sulfates which precipitate out of acidic aqueous solutions. It is therefore thought that the different mineralizations at different levels reflect the conditions that were present, including the changing characteristics of water that may have been in the crater. However, multi-spectral analysis only tells you the possible candidates for the actual rocks on site, while the mass spectrometer sent with Curiosity (actually, the largest instrument on the rover) will determine the detailed actual elemental compositions and ratios. If the mass spectrometer data supports the multispectral analyis, then a significant part of the history of that planet can become decipherable.
This work relates to our situation on Earth, because the models for climate evolution on Mars have some commonality with the ones used for Earth, and being able to validate some of the model predictions against the "ground truth" would allow more confidence in underlying modelling. A very interesting observation has been made that the hydration of the earth has apparently enabled the plate tectonics that make our planet so "lively". Neither Venus (which is very close in size to Earth), nor Mars have any observational evidence of plate tectonics, and there is speculation that both planets may have lost their water early in the history and that loss impacted the ability of the mantle and crustal rocks to support plate tectonics. If Mars NEVER had any sizable amount of water, then the lessons are less clear. If, on the other hand, Mars had a substantial ocean of water shortly after its formation, then the question becomes what happened to that water, and why/where did it disappear. The mission that Curiosity is on is supposed to help determine the answers to those questions.