Mode-locking is a very smart technique used for generating very short and intense light pulses with a laser.
Continuous lasers are usually thought as devices emitting light that is spectrally very narrow. And indeed, many applications use this monochromaticity of laser light to their advantage.
But a laser will naturally emit light over a spectrum much broader than that of a single longitudinal mode, even much broader than the spacing between modes. As a consequence, many longitudinal modes may oscillate simultaneously. Each of these modes may be thought of as an harmonic oscillator, but these oscillators are independent from one another : each one of them has a well defined frequency and phase, but there is no relationship between the phases of any two of these oscillators. As a consequence, the temporal behavior of the laser is very chaotic : seen on the screen of an oscilloscope with enough bandwidth, the beam intensity is not steady, but extremely noisy instead.
The situation would be quite different if one could maintain a fixed relationship between the phases of the modes. One could manage to have, at any one point in space, all the modes reach their maximum intensity at the same time, thus creating peak in intensity with very high power. Because average power of the laser would remain the same, this means that the rest of the time, the intensity of the beam would be close to zero : the laser emission is now made out of short pulses separated by periods of zero laser emission.
It is in fact possible to "lock" phases of modes inside a laser cavity. This is usually achieved by creating an periodic phase modulation inside the cavity with an acousto-optic modulator. As long as lasing goes on, the laser will emit short pulses, regularly spaced in time. One talks then about a "train" of pulses".
What is the spacing between two consecutive pulses ? The answer to that comes from the fact that what you believe to be a train of pulses is in fact always the same pulse. Upon hitting the output mirror, part of the pulse leaves the laser cavity to become the next pulse in the train. The reflected part of the pulse goes back into the cavity to undergo an amplification that will regenerate its energy. Aftyter a round trip in the cavity, it will reach the output mirror again, and the transmitted part will be the next pulse of the train a.s.o.... So it is clear that the distance between two consecutive pulses in the train is twice the cavity length. Divide that by the speed of light, and you have now the time difference between two pulses.
What is the duration of each pulse ? This answer to that is a bit more complex. Fourier analysis tells us that a pulse can be no shorter than, to put it shortly, the inverse of its spectral bandwidth. Well engineered mode-locking will indeed get close to that limit. So the duration of the pulse in in fact determined by the spectral width of the lasing medium : the broader the spectrum, the narrower the pulse. Broad emission media (e.g. dyes, or Ti : Sapphire) will readily lead to picosecond pulses (10E-12).
Note that further tricks (beyond genuine mode-locking) can generate pulse durations down to just a few femtoseconds (10E-15).