Related: Immune
I much better understand the necessity of the lymphatic system after reading Immune and realizing that the circulatory system is closed in vertebrates.
The circulatory system uses plasma as a medium to exchange from the red blood cells to the surrounding tissues. Because of this, there is some leakage - not all the fluid gets taken back when the blood exits through the veins. The lymphatic system is sort of the drainage pipe which takes the leftover plasma and transfers it back to the circulatory system.
The cool part is that this leftover plasma also contains a lot of information from the cells which can be used find the state of the tissues - if they are healthy, damaged or have an infection.
The immune system uses this information to recruit more cells and mount attacks, which looks a cool side-effect of having a slow drainage system!