The weeks surrounding perihelion are extremely important. The comet's levels of activity (melting and spewing gas, for example) have been going up steadily, and this time will give scientists access to crucial data that might otherwise have stayed locked away in ice. In fact, the highest activity levels aren't expected to happen on perihelion, exactly. Proximity to the sun will warm the comet up more over time, so it's hard to say when the comet will have its peak day of spewing gas and vapor.
On July 29, the Rosetta orbiter caught sight of some of this vigorous activity:
It is likely that activity will peak a few weeks from now. After that, as the comet cools, Rosetta will come back in for a closer orbit to study how the comet has been changed by the close encounter.
Meanwhile, it is unlikely that Rosetta's lander — the much beloved Philae, which lost power because of a bumpy landing that placed it in the shade but woke up recently thanks to increases in sunlight — will get back in contact with Earth.
Using data from Rosetta (and the data Philae was able to collect during its short but busy tenure), scientists hope to get a better understanding of how comets form and how they evolve over time. Because comets were formed in the very early days of the solar system, it is thought that their icy cores contain the molecular building blocks available 4.6 billion years ago. Revealing these could help us understand how the entire solar system — including our own planet — was formed.