Click here to view the sky from the North Pole where this effect is at its most extreme. From here, the entire sky is circumpolar.
Press the P button in the Time and Date display to start time running, and you'll see that no stars rise and no stars set; they all remain visible all the time, and each star maintains a constant altitude above the horizon. The North Star cannot be seen because it is directly overhead.
Remember that the altitude of the North Star is equal to your latitude, which is now 90 degrees north. If you scroll up in the sky, you can see the North Pole almost exactly at the zenith.
Click here to move around to the south and find Saturn and Jupiter. If you follow their motion, you can see that they (like all the planets, as well as the moon and the sun) also circle endlessly at a constant elevation, neither rising or setting.
The downside of being at a location where all stars are circumpolar is that many stars and constellations that are prominent from mid-northern latitudes cannot be seen at all.
You can click here to find Rigel, but a window will come up to tell you that Rigel is beneath the horizon. You can keep running time forward forever, but this bright star in Orion will never come above the horizon.
From any location, half of the sky is visible at any given moment. But the closer you are to the equator, the greater the number of stars that rise and set, meaning that you can see more different stars, but they are above the horizon for a shorter period of time.