Diagram of radiation belts from NewScientist magazine.
This antimatter exists within the inner Van Allen radiation belt. The particles that are not instantly destroyed by touching regular matter get trapped by the Earth's magnetic field, holding them in a torus around the Earth. Here the particles have a much better chance of remaining for an extended period of time because there's not as much matter for them to interact with.
These antiprotons are thought to be created when cosmic rays interact with the Earth's atmosphere. Most often regular matter is created by these interactions, which serves to populate the Van Allen belts, but every now and then an antiproton will be created. Most of this antimatter is instantly destroyed upon impact with regular matter, but some of it manages to safely reach the inner Van Allen belt where it can exist for a while longer. Even with this low production rate, there is estimated to be more antimatter within the Van Allen belts than in any cosmic ray.
Example of cosmic rays
In 2006, PAMELA (Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics) was launched to find this antimatter which had been theorized to exist. It orbited for 850 days and managed to pick up 28 antiprotons. This might sound like a very small amount, and it is, but it is much more antimatter than we can find anywhere else. One must also take into account that this probe only explored an incredibly small fraction of the Van Allen belts, so there's bound to be much more antimatter out there.
PAMELA space probe
The upshot of all this is that some reporters are saying that this antimatter may be enough to eventually fuel antimatter rockets. It's hard to tell if this is true or just an artifact of science reporting, but one thing is for sure, it's very exciting.
Antimatter rocket from HowStuffWorks.com