An action potential triggers the vesicles in the pre-synaptic dendrites to burst and release their neurotransmitters into the synaptic gap where they diffuse across and bind with receptors on the post-synaptic dendrite.
Any excess that doesn't bind gets taken back up into the vesicles to await the next action potential.
Excitation / inhibition depends on the neurotransmitter that is released: adrenaline and dopamine are excitatory neurotransmitters, so when they are released, diffuse across the gap and bind to receptors, they excite the next axon and so messages get passed on.
However, serotonin and GABA are inhibitory neurotransmitters, so when they are released, diffuse across the gap and bind to the receptors, they inhibit the next action potential so messages slow down.
This explains why a lack of serotonin at the post-synaptic membrane (perhaps due to excessive reuptake) is associated with the high brain activity of repetitive, intrusive thoughts in anxiety, depression and OCD.
Using SSRIs to inhibit (reduce) reuptake allows more serotonin to bind to receptors, and can alleviate the symptoms and slow the thoughts, calming the brain.