The Planck length is the scale at which classical ideas about gravity and space-time cease
to be valid, and quantum effects dominate. This is the 'quantum of length', the smallest
measurement of length with any meaning.
And roughly equal to 1.6 x 10^{-35} m or about 10^{-20} times the size of a proton.
The Planck time is the time it would take a photon travelling at the speed of light to
across a distance equal to the Planck length. This is the 'quantum of time', the smallest
measurement of time that has any meaning, and is equal to 10^{-43} seconds. No smaller
division of time has any meaning. Within the framework of the laws of physics as we
understand them today, we can say only that the universe came into existence when it
already had an age of 10^{-43} seconds.
Answered by: Dan Summons, Physics Undergrad Student, UOS, Souhampton