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    consider the system used in this video (piston with a weight at the top being balanced by gas inside):
    consider this video
    (you just need to see the picture of the system, a piston thing)

    The requirements for a system to be considered reversible is that it is quasi static (have an infinite sequence of equilibrium states all infinitely close together) and need the absence of factors that could take energy away other than work for example... e.g. friction.

    on a P-V diagram, instead of having two lone points representing the initial and final state, for a system to be quasi static there would be many points in between these such that you can draw a line connecting the initial and final state.

    The latter requirement i can understand. if you lose energy due to friction in a process, then you cannot go back to your initial state. However i do not understand why a system needs to be quasi static...

    to make the system quasi static he replaces the giant weight with many small pebbles. this means when he takes a small weight out (instead of a big weight), the system wont be thrown out of equilibrium and hence have still have well defined variables. As a result, on the P-V diagram, he can draw a line between the two points... by why is this line important?

    if he takes half the weight off, the system will be kicked out of equilibrium BUT eventually come back given enough time... then you will have well defined variables again. if he puts all the weights back, he will kick the system out of equilibrium but at some point, it should go back to equilibrium, back to the initial state... hence you can reverse the process... there being no friction is the only important thing to consider here, so why does a system need to be quasi static?
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