What might show between Ukraine and Belarus, if the diagram is done well, is a midnight line, so it's (say) 11 p.m. to the east of that time zone boundary, and midnight on the other. That's how we normally think of today and tomorrow: the official day starts just after midnight, even if mentally you count it as "today" until you go to sleep, even if that's at 3 a.m. The difference there, like the difference between Eastern and Central time in the U.S., is one hour. If you cross that line, you'll adjust your watch by one hour.
At the international date line, the difference is 24 hours. Instead of going from 10:30 Tuesday to 9:30 Tuesday, you go from 10:30 Tuesday to 10:30 Wednesday.
The time doesn't change at the prime meridian. Greenwich is (very approximately) in the middle of its time zone (Greenwich Mean Time).
OK, more detail than you might be looking for: time zones average 15 degrees of longitude wide, and theoretically centered on 0, 15, 30,...180 degrees either east or west of Greenwich. If you're near one edge of a time zone, that affects clock time at sunrise and sunset. Most people don't pay a lot of attention to that level of detail--you're more likely to notice that the days are getting longer than what the clock says when the sun is highest in the sky.
As VorFemme notes, a lot of the time zone boundaries are either slanted, offset from the longitude lines they "should" be on, to keep cities, states, provinces, and countries together. Alaska used to be three time zones; the entire state is now on one time zone. All of China is a single time zone, and keeps Beijing time, at least on paper and for purposes like train scheduling.