I've found a reasonable explanation on Wikipedia...
SSRIs are believed to increase the extracellular level of the neurotransmitter serotonin by inhibiting its reuptake into the presynaptic cell, increasing the level of serotonin in the synaptic cleft available to bind to the postsynaptic receptor.
But I'm confused about one thing. The whole point of reuptake is that after serotonin (or any other neurotransmitter) binds to the postsynaptic receptors, it has to vacate the receptor so that other signals can be conveyed. If SSRIs inhibit the reuptake of serotonin, it remains in the synaptic cleft... but then what happens?
Do the serotonin molecules bind to the receptors multiple times, since they keep on ending up in the synaptic cleft? If so, when would this end, and how would it affect the signal across two neurons?