There are a total of 10 areas in the Black Tower. You can't use items while you're inside (other than held items), or even go into your bag, but you do gain EXP and some money from each battle, making it a good place to train in. You won't be able to heal, but you don't have to clear all 10 areas in a row; once you've cleared one, you'll be taken outside, healed, and are then able to visit the next area or revisit a previous one.
The areas and Trainers inside are random, aside from the Boss Trainers, who remain the same every time. In each area, you need to track down the Gate Trainer, who will unlock the gate to the Boss Trainer, who you must fight in order to clear the area. You may also find a Nurse or Doctor to heal your Pokemon up if you can win against them, but keep in mind they will heal your Pokemon only once per trip through the area, so you should save their healing for a time when you need it.
Key to the City
After you've cleared Area 5, you'll receive the Tower Key that unlocks Black City. While this may not be important to you if you are playing Black 2, which is where you unlock the key in, it can be sent to a White 2 version using the Key System's Send & Receive Keys feature to grant them access to Black City and Black Tower, which are not normally accessible.
After beating Benga, when you return to Area 10, the Boss Trainer is replaced.
Shiny Prize for Beating Benga
After beating Benga in Area 10 of the Black Tower, you can return to Alder's House in Floccesy Town, where you'll be rewarded with a Shiny Gible for your victory.