'Rushing' a room involves making a room that produces resources (generator, water purifier, etc) produce it immediately in addition to a caps reward.
Simply select a room and press
. This will bring up the rush confirmation screen, which also shows you the probability of success, and press
. Rinse and repeat 50 times.
As the description suggests, failed rushes will not count, and failure will also have negative side effects on your vault such as Radroach attacks and fires, which in turn decrease your vault dwellers health and happiness, so if the probability is over 50%, don't chance it, and wait for the probability to be in your favour, which is about 45-47%. The probability will decrease over time, so it's best to be patient.