Time zones exist largely to keep clock time roughly matched to daylight, but the match is never perfect, and how far off it gets depends on where you are relative to your zone's boundaries and the season of the year.
Why sunrise time varies so much by location
Within any single time zone, locations at the eastern edge see the sun rise noticeably earlier than locations at the western edge, since the zone spans up to 15 degrees of longitude (roughly an hour of the sun's apparent movement) but everyone inside it shares the same clock time.
Why sunrise and sunset shift with the seasons
The Earth's axial tilt means the sun's arc across the sky changes throughout the year. The effect is strongest far from the equator: cities near the poles can see daylight stretch to nearly 24 hours in midsummer and shrink to just a few hours in midwinter, while equatorial cities see almost no seasonal change in day length at all.
How Daylight Saving Time tries to help
Shifting clocks forward an hour in spring effectively moves an hour of morning daylight to the evening, when many people find it more useful for outdoor activity after work or school. The tradeoff is a darker morning, which is one of the main criticisms of the practice, especially in more northern latitudes where winter mornings are already dark.
A quick way to estimate sunrise/sunset shift
As a rough rule of thumb, moving about 15 degrees of longitude east or west within the same time zone shifts true solar noon by about an hour relative to clock noon. Combined with seasonal effects from latitude, this is why two cities in the "same" time zone can have sunrise times that differ by 30 minutes or more.