What is a great circle track?
 

Definition:
A great circle is a line of shortest distance between two points on a sphere (or a flat surface) with a constantly changing track direction as a result of convergence.

What i don't get is why it refers to sphere as apposed to the earth?
and also why you constantly change direction as a result of convergence?

Because as a "first approximation" (in other words "roughly speaking") the Earth is a sphere.

Your're not really changing direction, you were right first time when you said you have " a constantly changing track direction". Because the meridians/lines of longitude converge towards the poles they are not parallel ( again because the Earth is a sphere) the angle a great circle makes to the lines of longitude ( your track) changes as you progress along the great circle.

To visualise this take a globe, try stretching an elastic band in a straight line between say LAX and London and see how the angle between the band and the meridians, your track, changes as you progress along the "route". If you get it right you "leave" LAX tracking to the northeast, somewhere along the route you will be tracking east, and near London your track will be southeasterly - but your great circle has always been a straight line.

( and before someone points it out there's at least one exception to the track changing direction rule - the equator).

Thanks alot for your help Twiggy, i got a globe out and it actually makes sense now. Cheers:)

A good website for helping you visualise it too is Great Circle Mapper

Great Circle Mapper

Thanks for that link Kestrel