How big is Phobos? 
Phobos is actually quite tiny compared to most other moons in the Solar System. It is not a round sphere-like object, but irregularly shaped, more like a lumpy potato. At the largest extreme, it is 26 km across, and the smallest is about 18 km across. Basically about the size of a large city here on the Earth.
What is its surface like? 
From the basic appearance, it is very much as it would look on the Earth's Moon, except that the surface features are exaggerated. Just like the Earth's Moon, Phobos has no atmosphere. Also like the Earth's moon to the Earth, Phobos has one face that constantly points the same direction toward Mars, and is called tidally locked.
One big difference you would notice is that there is almost no gravity at all on Phobos. Just by jumping with your own legs, you would be able to put yourself into "orbit" and "fly" around Phobos. The gravity is only 1/1000th as strong as it is on the Earth. This also affects "mountains" on Phobos, as there would appear to be huge cliffs and other features where on even the Earth's Moon they would have collapsed due to gravity pulling them down.
One of the most prominent features on Phobos is a giant crater named Stickney. The impact from this crater has a significant effect on the structure of the entire moon, and there are lines or "grooves" along the surface of Phobos that were formed as a result of this impact.
If you were standing on Phobos, Mars would be a significant feature in the sky, taking up almost 1/4 of the sky.
How long is a day on Phobos? 
A day on Phobos is the same as its orbit around Mars, because it is tidally locked. This is about 7 hours 40 minutes.
How long is its orbit around Mars? 
Phobos is very close to the surface of Mars. In fact, it is closer than any other moon in the Solar System that has been discovered so far from the surface of the planet that it orbits.
The time it takes to go around Mars is about 7 hours and 40 minutes. This produces a very interesting experience to somebody on Mars, where Phobos rises from the west and sets in the east, as it travels faster than the Sun on a Martian day. Phobos' orbit is about 3 seconds faster than Deimos, which you will read about next.
Does Phobos cause a solar eclipse on Mars? 
Just as on the Earth by the Earth's Moon, Phobos does eclipse the Sun on Mars. This is also called a transit, and produces many of the same effects that you see from a solar eclipse. If you were to see such an eclipse on Mars, it would significantly darken the Sun, but it would not go into totality as the Earth's Moon does on the Earth. This is because Phobos is too small to cover the Sun completely. Also, because the orbit of Phobos is so fast, the eclipse would happen very quickly, in just a few seconds instead of the several minutes you see an eclipse on the Earth.
Because Phobos orbits Mars so closely, an eclipse near the Martian equator will be much more noticeable than an eclipse further north or south, because Phobos is usually quite a bit closer to an observer at the equator.
Is there a future for people on Phobos? 
Because Phobos is so close to Mars, and because of the very low gravity, Phobos may be a place where people and supplies are transferred before going to the surface of Mars and then going to the Earth, almost like a space station in orbit around the Earth. It is very likely that if people go to Mars as astronauts, they will be visiting Phobos as well. Phobos also has frozen water that could be useful to astronauts on Mars as drinking water and for extracting oxygen to breathe.
However, Phobos is a doomed world. In about 50 million years, it will not exist. Every year, it gets about two meters closer to the surface of Mars, and will eventually crash or be ripped apart, forming a ring around Mars which will eventually fall to the ground.
Who is it named after? 
Phobos was named after the son of Mars, who in mythology was the god of "fear" or "fright", and one of the servants of Mars.
How was it discovered? 
Asaph Hall was an astronomer with the United States Naval Observatory, where he studied many of the planets and objects in the Solar System. In 1877 he discovered both Phobos and Deimos, and identified them as moons of Mars. The name for Phobos was suggested by Henry Madan, based on the book Iliad, a classical Greek book about mythology. His wife's maiden name, Stickney, gave the name of the giant crater.
How much will Phobos' gravity pull on me? 
Phobos, because it is so small, has hardly any gravity at all. It has so little gravity that a 100-pound person on Phobos would only weigh 1/20 of a pound. This also means that you would be able to lift massive amounts of mass. A person who could carry 10 kg on Earth would be able to carry three elephants on Phobos.
Because Phobos' gravity is so small, it is easy to escape Phobos and float off into space. In fact, Phobos' gravity is so light that you could throw a tennis ball or a baseball and it would fly away from Phobos and become a new moon of Mars!