Rise time is the time taken by a laser beam to travel from a lower specified amplitude value to a higher specified amplitude value. Usually, the lower and higher amplitude values are taken to be 10% and 90% of the peak value of the laser pulse. So, basically, the rise time is the time taken by a signal to go from 10% to 90% of the peak amplitude value of the signal.

If we consider the upper limit and lower limit to be two states of a signal, then rise time measures the time taken to switch from the low state to the high state. 

Fall time is the time taken by a laser beam to travel from a higher specified amplitude value to a lower specified amplitude value. Usually, the lower and higher amplitude values are taken to be 10% and 90% of the peak value of the laser beam. So, basically, fall time is the time taken by a signal to go from 90% to 10% of the peak value of the signal.