Jet lag (ICD-10: G47.2) occurs when the body's internal clock (its circadian rhythm) gets out of sync with the time of day.
Example: London to Los Angeles
Leaving London at 1200 you will arrive in Los Angeles ten hours later and your body will feel like the time is 2200. The actual time will be 1400 and so your body expects it to be late night, but it's actually the middle of the day: an offset of eight hours. Travelling back, leaving Los Angeles at 1200 you will arrive in London ten hours later and again feel like the time is 2200, but it will actually be 0600 the next day; your body expects late evening but gets early morning: an offset of sixteen hours. The difference in these offsets is what gives rise to the fact that travelling west to east causes worse jet lag than travelling in the opposite direction.
Jet lag only occurs when travel causes a difference between the internal and real clocks. If you take anything more than one hour to travel a time difference of one hour then jet lag does not occur. Also, flying north to south doesn't cross any time zones and therefore jet lag does not occur; flying from Cape Town to Stockholm, for example, is safe for your body clock.
The Earth rotates once per day and therefore contains twenty-four time zones, spaced evenly apart. Turning through 360° in twenty-four hours is equivalent to 15° per hour. At the equator, fifteen degrees of longitude is equivalent to 1670 kilometres so an aeroplane flying along the equator would have to travel at a speed of at least 1670 kilometres per hour (over 1000 mph) for jet lag to occur. At a latitude of 45° (north or south) this 15° is only 1180 kilometres, reducing the speed of jet lag to 734 mph.
Both of the situations above assume that plane fly directly along lines of latitude, but this never happens. In reality planes fly "great circle" paths (see the previous post about geodesics) and travelling along great circle paths, especially those that fly close to or over the poles where time zones are "thinner", lowers the speed of jet lag to below the 500-600 mph speed of an aeroplane.
The narrowing of time zones at northern latitudes is obvious in this map of Western Europe.