There are lots of mechanisms going on to explain paired pulse facilitation and depression. But the simplest to understand, and the most common place are:

Paired Pulse Facilitation (PPF) is due to the fact that release probability is highly sensitive to Calcium concentration. It is generally reported that the probability of a vesicle being release is proportional the the calcium concentration to the fourth power. This means that once you get into the range of calcium concentrations that cause release even a tiny increase in calcium concentration causes a huge increase in release probability. So, when you deliver two stimuli close together, the second presynaptic action potential happens before all of the calcium from the first presynaptic action potential has been cleared. This means there is more free calcium in the presynaptic terminal during the peak of the second action potential, which increases the probability of release, causing PPF.

Paired Pulse Depression is due to the simple fact that the first action potential reduces the number of vesicles available for release. Given that each vesicle has it's own probability of fusion, if there are less vesicles, then there is a reduced probability that a given terminal will release a vesicle.

These two ideas explain why synapses with a high release probability generally show PPD, and synapses with a low release probability show PPF: If you nearly always release a docked vesicle (high release probability) then there will be less docked vesicles at the second stimuli. One the other hand, if you don't release a vesicle, then the summation of Calcium can have it's effect. It also explains why during trains of stimuli, even synapses that show PPF will eventually depress: given a long enough train, docked vesicles will begin to be depleted.

Just to be clear, this is not 100% accurate, and FAR from an exhaustive explanation of presynaptic short term plasticity, but it seems like a good place to start. If you want an exhaustive discussion I suggest you read:

Short-term synaptic plasticity

RS Zucker, WG Regehr

Annual review of physiology, 2002

thank you Mr.William M Connelly

I will try to put it simply in my own words:

high release probability implies there will be many release-ready synaptic vesicles already primed at the active zones in the presynapse. Therefore many of them will be released with your first pulse stimulation. So the first response will be bigger than the second one (in the short time between the 1st and 2nd pulse, not so many vesicles could be made 'ready' for release)

with low release probability, there are not as many release-ready synaptic vesicles already primed at the active zones in the presynapse. In this case after your first pulse, there will be a build up of Ca2+ within the presynaptic boutons leading to priming and release of many more synaptic vesicles with the second pulse. So in this case the second response will be bigger than the first (paired pulse facilitation) as the initial release probability (or no. of release ready vesicles) was low and the facilitation was due to entry of Ca2+ after the 1st pulse.