Yes, per second per cubic metre. Pardon me.
Each one of those alpha particles that either the radon itself or the metals it produces or releases causes a packet of energy to get into any cell it's next to. Radon gas itself, because it doesn't react—it's inert chemically—tends to be farther away. The radon-related metals that it produces tend to be very close to the cell linings. When they also release these alpha particles, it's the alpha particles themselves that wreck the nucleus of the cell and that ultimately cause lung cancer.