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Work done on a system means that energy is being put into the system (endothermic) from the surroundings. Using the equation (at constant pressure) w=-P (Vfinal-Vinitial), work done on a system means that the final volume is lower than the initial volume producing a positive w. This means work goes into a system and thus is done on a system. Work done by a system means that energy is moved from the system into the surroundings (exothermic). Using the equation (at constant pressure) w=-P(Vfinal-Vinitial), work done by a system means that the initial volume is lower than the final volume producing a negative w. This means work is done by the system on the surroundings.
A simple way I think about this is: if you're in a box and pushing the roof away from you to make more space, then you (the system) is doing work on the surrounding (because it takes effort to push the roof). If the roof is pushing down on you (even though you resist) the roof (surrounding) is doing work on you (the system). I hope that makes sense. In one case, you're pushing, and in the other, you're being pushed.
Work done on the system means something outside of the system (the surroundings) did something to increase the internal energy of the system. Work done by the system means the system's internal energy decreased as it did work on something outside the system (its surroundings).
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