I am a beginner in electronics facing a bit more difficult problem.
The diodes keep the bases of the transistors 1.4V apart. This reduces crossover distortion. The resistors are to provide a bias current for the diodes.
So the diodes keep the transistors "close" to being on. If they weren't there, as the input voltage went between ~0.7 and ~-0.7V the transistors would be in cutoff and the output voltage would be zero. This causes the output to have distortion around the zero crossing. Keeping them biased on like this is called class AB operation.
Feedback can be useful to help minimize distortion, but class AB operation helps as well. Another technique often used is a Vbe multiplier instead of the two diodes. The Vbe multiplier allows more control over how much bias you are providing the output transistors. (Google it for more info.)
Often the diodes are mounted on the same heatsink as the transistors (or sometimes in the same package as the transistors) in order to track the change in forward voltage/Vbe with temperature.