The lymphatic system in your body is a second circulatory system, identical in almost every way to your arterial/vascular system except that it carries lymph instead of blood, and has no heart to pump it. Lymph is specifically evolved to move many of the active cells in the immune system, and so the lymph system is a very important part of your immune defense. Lymph is 'pumped' to the lymph nodes (under your arms, in your neck, in your groin) where the bad stuff (viruses, bacteria, cancer) is filtered out for further attack by the immune system.
In order to move lymph fluid through the lymphatic system, the body evolved the ingenious design of co-locating the lymph system immediately adjacent to the vascular system, but in the opposite direction. What this means is that the lymphatic 'tubes' have in them one-way valves (just as the arteries do), but those one way valves lie in the opposite direction to the adjacent vascular system. When the arteries or veins pulse with a heartbeat, part of that pulse is transmitted to the adjacent lymph system, and together with the one-way valves, that pulse is enough to 'pump' the lymph in its proper direction (to the lymph nodes).
Lymphatic drainage refers to a style of body work that massages away from the heart (opposite the direction of traditional massage) which, in theory, forces the lymph through the nodes faster. The technique requires a very high level of skill, training, and anatomic knowledge because, since you're massaging away from the heart, you are massaging in opposition to the blood flow of the veinous system, which is closer to the surface of your body (the deeper arterial blood flow goes the opposite way, away from the heart). Because you're working the massage pressure in opposition to the natural flow of this veinous system, you run the risk of damaging the one-way valves in your veins. Hence the need for the practitioner to really know what they're doing.
I've had this treatment many times and, when done right, it is one of the most powerful (and painful) therapeutic modalities. But, IMHO, it's hard to find the right therapist.
Now as to the prostate thing: that's when they stick a finger up your butt and wiggle it in an attempt to turn you gay.