Earth's orbit takes it around the Sun once every 365 days (which, of course, is the definition of a year). Mars is farther away from the Sun, which means its orbital path is longer and it travels along it more slowly. It orbits the Sun once every 687 days.
That's a bit less than two Earth years, so each time Earth goes around the Sun once, Mars has gone around a bit more than half of its orbit. This also means that every so often — specifically, every 26 months — Mars and Earth are lined up with the Sun, like this:
This configuration is called an opposition of Mars. (Oppositions happen periodically with any planet that is farther from the Sun than Earth is.)
You can see that because the two orbits are not perfectly circular, there are some places where the paths are close together and others where they're far apart. In August of 2003, Mars was at opposition and very close to perihelion (its orbit's closest point to the Sun). Because Mars was closer to the Earth in August of 2003 than it was during either of the previous oppositions (in June of 2001 and April of 1999) it looked bigger.
Below are the dates of the three oppositions, with corresponding views of Mars at the same magnification, and orbit diagrams showing the relative positions of Mars and Earth:
Now that you've read about how oppositions work, remember that email that someone forwarded to you, describing how Mars will look as big as the full Moon this coming August? Guess where that came from!
Someone wrote that in early 2003, before that really good perihelion opposition. Unfortunately they didn't mention the year, so everyone who sees that email for the first time thinks it refers to this year, and passes it on. But oppositions don't happen every August, and certainly oppositions that spectacular don't happen every time we swing by Mars.
Secondly, it was completely wrong about how big Mars would look during a perihelion opposition. During the 2003 opposition, its angular width in the sky was about 24 arcseconds. The Moon's angular width is around half a degree, or 1800 arcseconds — about 80 times the angular width of Mars at perihelion opposition. These emails usually get the distance completely wrong too — Mars was about 55 million kilometers away during the 2003 opposition.
Drag out your Pythagorean theorem and prove it for yourself, or consult an astronomer who was looking at it — or pop the following .snf files into your Starry Night to watch how Mars orbits and how its size changes over time when seen from Earth.