Roll period is how quickly a vessel return to upright position while rolling. So it is the time a ship takes from upright position to going to a particular angle on port side and then going to a angle on starboard side and then again returning back to upright position (zero list position) during natural rolling.
For example let us say a ship is rolling to around 20 degrees on both side and it is rolling in the following cycle.
1) From upright position to 20 Degrees to port side
2) From 20 Degrees port to 20 Degrees to starboard side
3) From 20 Degree starboard to upright position
If the Ship takes 10 seconds for this cycle to complete then rolling period of the ship is 10 seconds.
One of the formula for calculating roll period is
So the roll period depends upon the Beam of the vessel and GM of the vessel. To a certain extend it also depends upon the ship size and hull design.