Crew members aboard the ISS can observe as many as 16 sunrises and sunsets in a 24 hour period. But, as Wiseman notes in his Vine, the view from space changes considerably when the Space Station's orbit comes into alignment with the day/night terminator line, i.e. the barrier between light and dark on the surface of the Earth.

The angle between Earth's rotational axis and the plane in which it orbits the sun is 23.4°. This "axial tilt" causes one pole to be pointed toward the Sun on one side of the planet's orbit and the other pole on the other side. This means that the orientation of the day/night terminator line is constantly changing. (It also gives our planet its seasons.) In the footage above, the orientation of the terminator line along Earth's surface can be seen cycling through two solstices and two equinoxes in its annual, metronomic dance.

Image Credit: SAT-Flare via StackExchange

In the image above, the orbit of the ISS appears in red and the day/night terminator in dark blue. When the two align, astronauts aboard the ISS experience a never-setting sun. This happens in the weeks bookending the summer solstice, the date on which Earth's North pole is tilted the full 23.4 degrees toward the sun. (This year's summer solstice will occur on June 21st.)When this angle is added to the Space Station's orbital inclination (i.e. the angle at which a satellite orbits relative to Earth's equator, which, for the ISS, is 51.65°), the ISS avoids Earth's shadow entirely, and you get a view like the one captured by Wiseman. More detailed explanations exist for those unintimidated by orbital mechanics, but I'm fond of this description from astronomy blogger Bob King:

In the diagram, the circle represents Earth with its north pole tipped sunward around the time of summer solstice. The ISS's orbit – tipped well up from the equator – is shown in profile. Notice how close the station passes to the day-night line or terminator. This allows it to remain in sunlight its entire orbit. Image and Caption Credit: Bob King

Earth's axis points off to the left with the northern hemisphere tilted toward the sun. The terminator is the boundary between day and night on the planet, and the equator cuts perpendicular to the axis. The space station's tipped orbit places it very near the terminator this time of year, high enough for it to catch the sun's rays all night long.

Altogether, not a bad subject at all for history's first space-Vine. Big props to Wiseman for this one.