The lecture about comets was going to be a week later, but I gave it earlier because of the media coverage of the Philae landing on comet 67P the previous day.
Comets are one group of small bodies of the solar system. They consists mostly of rocky material, dust and various ices (mainly water and carbon dioxide). Comets orbit the Sun, and when they approach close enough to it, they warm up enough for some of the icy materials to sublimate. This causes an outburst of dust and gas, which causes the large and bright tails of comets. These easily sublimating materials on the comet are called "volatiles".
The difference between comets and asteroids is somewhat blurry. A comet is defined generally as a small body showing this kind of outburst activity. Some bodies have been originally classified as asteroids but later reclassified as comet-like behaviour happens. On the other hand, old comets may eventually lose all of their volatiles, becoming just rocky bodies which would be classified as asteroids.
Comets originate in a region known as the Oort cloud. It is located very far from the Sun, in the outer reaches of our solar system. The Oort cloud is a huge collection of icy bodies like comets, which remain there since formation of the solar system.
Sometimes, objects from the Oort cloud fall into the inner solar system towards the Sun. They fall on very long elliptical orbits, taking thousands or tens of thousands of years to complete an orbit towards the Sun and back to the outer solar system. These objects are known as the long-period comets. They may also be on hyperbolic orbits, which pass by the Sun once and never return.
Due to the gravitational effects of Jupiter, long-period comets may change their orbits and end up orbiting nearer the Sun. These comets orbit the Sun in a number of years or decades. These are known as short-period comets. The most famous short period comets include Halley's comet, which orbits the Sun roughly every 76 years, and now Rosetta's target comet 67P/Churyumov-Gerasimenko, with an orbital period of 6.4 years.
Comets are generally named after the astronomers or the observatory which finds them.
An active comet exists on three very different size scales. The actual comet body, called the nucleus, is relatively small, typically hundreds of metres to some kilometres in size. As described above, it consists of rock, dust and ice in a varying mixture.
As the volatiles on the comet are released, they form a cloud of dust around the nucleus. This cloud, known as the coma, can be tens or hundreds of thousand of kilometres across, or even larger.
The solar wind interacts with the coma, blowing it away from the Sun. This causes the coma to stretch into a tail. Comets have in fact two different tails: the gas in the come is much lighter than the dust, and gets blown directly away from the Sun as a gas tail. The dust, being heavier, has more inertia and generally lags slightly behind in the comet's orbit. These two tails overlap to a varying degree.
The dust produced by comets remains in orbit around the Sun, forming a dust band. Now and then the Earth passes through a dust band, which is seen on Earth a meteor shower, when the number of dust grains hitting our atmosphere is higher than usual for a while.
Rosetta is a space mission by the European Space Agency. It was launched in 2004 and traveled for 10 years in space in a complicated but fuel-efficient trajectory until arriving at comet 67P/Churyumov-Gerasimenko earlier this year.
So far it has orbited the comet and done various scientific measurements. On November 12th, Rosetta released a separate lander spacecraft called Philae. The landing of Philae did not succeed perfectly, but it did achieve most of its science goals and is generally considered a success. Philae is powered by solar panels and is currently out of electrical power due to landing in a spot with poor illumination, but it may wake up in the future as the comet nears the Sun.
Rosetta entered its main science phase after the release of Philae and will continue to observe the comet in detail as the comet approaches the Sun and becomes more and more active.