What do the lines on a Feynman diagram represent? I know that the lines do not represent the paths of the particles, so what do they represent, please?
I have looked on the Wikipedia article, but it seems confusing that particles can move backwards in time - surely if they are colliding, they would move forwards towards the point at which they collide. The image on Wikipedia shows a positron moving backwards from the collision. I am also confused by the probability amplitude - I have seen websites discussing it in terms of complex numbers.
Update: From what I have seen so far, I'm getting the impression that these lines represent possibilities for decay (I think that's what decay channels are?), but I am still not sure about why some particles move against time.
Update 2: The idea that the lines represent probabilities and that we can multiply probabilities on each line to give a total probability for the whole event makes me think that this is like a probability tree.
 A: For most applications especially in experimental physics you can think of the lines as particle trajectories in time and 1D Space. All particles travel forward in time, you might refer to the Feynman-Stueckelberg-Interpretation where particles with negative Energy are interpreted as particles moving backwards in time but this is just an interpretation and it can also be seen as an anti-particle traveling forward in time.
An Example:

This is one possible feynman-Diagram of infinitely many ones describing two electrons scattering. Sum all the possible Diagrams up and square them, integrating them over the phase space and you will get the Probability for this process to happen.
More carefully is a Feynman-Diagram the symbolic expression of the scattering amplitudes in a quantum field theory for one possible process and at a specific pertubation order. The lines are the "propagators" for the specific theory you are considering which can be calculated from the lagrangian of the theory. So when people draw a feynmandiagram they actually write down a algebraically complex formula. 
