What causes the sun to rise?

Although the Sun appears to "rise" from the horizon, it is actually the Earth's motion that causes the Sun to appear. The illusion of a moving Sun results from Earth observers being in a rotating reference frame; this apparent motion caused many cultures to have mythologies and religions built around the geocentric model, which prevailed until astronomer Nicolaus Copernicus formulated his heliocentric model in the 16th century.
Astronomically, sunrise occurs for only an instant: the moment at which the upper limb of the Sun appears tangent to the horizon. However, the term sunrise commonly refers to periods of time both before and after this point:
Twilight, the period in the morning during which the sky is brightening, but the Sun is not yet visible. The beginning of morning twilight is called astronomical dawn.
The period after the Sun rises during which striking colors and atmospheric effects are still seen.
The timing of sunrise varies throughout the year and is also affected by the viewer's latitude and longitude, altitude, and time zone. These changes are driven by the axial tilt of Earth, daily rotation of the Earth, the planet's movement in its annual elliptical orbit around the Sun, and the Earth and Moon's paired revolutions around each other. The analemma can be used to make approximate predictions of the time of sunrise.
In late winter and spring, sunrise as seen from temperate latitudes occurs earlier each day, reaching its earliest time near the summer solstice; although the exact date varies by latitude. After this point, the time of sunrise gets later each day, reaching its latest sometime around the winter solstice. The offset between the dates of the solstice and the earliest or latest sunrise time is caused by the eccentricity of Earth's orbit and the tilt of its axis, and is described by the analemma, which can be used to predict the dates.
Variations in atmospheric refraction can alter the time of sunrise by changing its apparent position. Near the poles, the time-of-day variation is exaggerated, since the Sun crosses the horizon at a very shallow angle and thus rises more slowly.
Accounting for atmospheric refraction and measuring from the leading edge slightly increases the average duration of day relative to night. The sunrise equation, however, which is used to derive the time of sunrise and sunset, uses the Sun's physical center for calculation, neglecting atmospheric refraction and the non-zero angle subtended by the solar disc.

Although the Sun appears to "rise" from the horizon, it is actually the Earth's motion that causes the Sun to appear. The illusion of a moving Sun results from Earth observers being in a rotating reference frame.