As seen in the replies, some plastic surgeons feel that breast "massage" is not necessary, but most experienced breast surgeons feel that implant movement exercises help to keep the submuscular pocket created to enclose the implant larger than the implant, reducing the likelihood of capsular contracture. Capsular contracture is tightening of the scar capsule around the implant, making the breast(s) feel firm.
BTW, this answer assumes smooth implants (saline or silicone), since textured implants, like the teardrop "anatomic" or the "gummy bear" implants, are designed to adhere to the tissues and NOT move. This is because shaped implants rely on being in a specific position to look "normal" or "anatomic" and would look silly if upside down, for example!
BREAST IMPLANTS DO NOT HARDEN, EVER.
However, the scar capsule around your implant(s) can thicken or tighten (caused usually by bleeding or bacteria), making your breasts firm or unnaturally-shaped. Careful surgery, in my opinion, is important to avoid bleeding or bacterial contamination that can lead to excessive capsule formation (capsular contracture), and keeping the surgical pocket mechanically open with careful implant movement exercises can reduce both the incidence and severity of capsular contracture, should it occur.
I have my patients begin gentle implant movement exercises every three hours (when they take their muscle relaxant) while awake, simply pressing on the lower pole of the breast to force the implant to slide upwards in the already-created pocket. I have patients go braless until the implants have dropped into position, after which a bra is worn to prevent further drop or bottoming out. I believe implants should be moved in their pocket until complete healing has occurred (several months), and after a few weeks, can be done while showering or through clothing in the restroom.