Pumping, in the context of BE, is the use of suction devices to increase the size of a person's breasts.
Like implants, there is in fact sound science and clinical trials behind the use of such devices and most if not all women will experience results if the program is followed. Unlike implants, however, the largest size that can be achieved through the use of pump devices is limited by the size of the domes produced for the unit in question.
Suction devices work by stretching out the breast tissues which, over time, results in new cells being formed. It is common for women using such a device to experience swelling during and shortly after a treatment where their breasts are considerably larger than normal; the swelling will decrease over the course of the day.
It should be noted, however, that results using a suction device will not be immediate. Brava requires that the unit be worn for at least 10 hours a day (ideally while sleeping) for 10-14 weeks for one cup size of growth. Even using higher-suction options such as Bosom Beauty 2012 or Noogleberry will require an investment of at least an hour a day.
Using these devices can be painful and will take time out of the user's day, so be sure you are prepared for both if you plan to purchase or use such a device.
The Brava system was developed by Dr. Roger Khouri and is the only suction device backed by a guarantee and clinical trials. The unit is expensive, but not as expensive as surgery. It is designed to be work for 10-14 hours per day; a wear period of 10-14 weeks is generally sufficient for increasing breasts by about 100cc.