The heliosphere is the giant bubble of gas that surrounds the sun. The solar wind is charged particles coming out of the sun in all directions. It fills the space around the sun with gas, and it forms a humungous bubble, bigger than the whole solar system.
Even though it's huge, that bubble has an edge. That edge is called the "heliosheath." To see how the heliosheath forms, you can try a simple experiment.
In an empty sink, turn on the faucet so a stream of water pours down on a flat part of the metal basin. Then examine the water. You'll see that in the middle, where the stream is landing, the water is thrust out strongly in all directions, making an even sheet. This corresponds to the solar wind close to the sun, where it pushes gas away in an even manner.
The farther you go from the center, though, the less powerful the pressure is, because it's covering a wider area. The result is that the water starts to become turbulent, because there isn't enough force to push it all away evenly.
Suddenly, at the edge you will see a wobbly ring form. The ring occurs at the point where the pressure of the water going out can't overcome the pressure of water trying to go in other directions. In space, that ring is the heliosheath.