The heliosphere is a large bubble in space created by the solar wind from the Sun. At the fringes of the heliosphere, the solar wind collides with gases from the interstellar medium and stops being the dominant space weather. The heliosphere is huge -- its closest boundary is about 100 AU (astronomical units, or Earth-Sun distances) away, while its farthest boundary its 200-300 AU distant. The heliosphere is shaped elliptically, like the tail of a comet, because of the Sun's fast motion through the interstellar medium as it orbits the galactic center.
As stated, the cause of the heliosphere is the solar wind. The solar wind is a continuous stream of charged particles, mostly free electrons and protons, which flow from the Sun at a velocity of 400 to 700 km/s (about 1,000,000 mph). This works out to 6.7 billion tons per hour, or a mass equal to the Earth every 150 million years. While this sounds like a lot, it is actually very diffuse due to the vastness of space.
Besides the solar wind, the heliosphere is also maintained by the Sun's magnetic field, which extends outwards at least 100 AU, and has a shape similar to that of the dress of a spinning ballerina due to the Sun's rotation every 27 days. This structure, the heliospheric current sheet, creates a ripple in the entire heliosphere, and along with the heliosphere itself, is the largest structure in the solar system.
Besides the heliospheric current sheet, the heliosphere has other structure. For instance, there's the termination shock, a boundary about 70-90 AU from the Sun where the solar wind goes from being supersonic to subsonic. This boundary was crossed by the space probe Voyager II in 2007. Actually, the probe passed it five times, because the boundary fluctuates due to corresponding fluctuations in the solar output, including solar flares. In space, the speed of sound is far faster than on Earth (about 100 km/s), so the solar wind is still moving quickly at this distance, just not quickly enough to exceed the speed of sound.
Farther out than the termination shock is the heliopause, where the charged particles in the solar wind collide with the particles of the interstellar medium, and the bow shock, where the solar wind ceases to have any effect on the interstellar medium at all. Neither has yet been reached by our space probes, but they will be by 2020. In addition, the Interstellar Boundary Explorer, launched in 2008, will provide valuable information about the interstellar boundary.