Most of serotonin exists outside of the brain and is involved in regulating the gut and blood clotting. However, you seem interested in what's going on in the brain so I'll go into that.

Almost all serotonin is made in the raphe nuclei (a cluster of cells) out of a chemical called tryptophan. From there, it is sent to various other areas of the brain involved in regulating all sorts of stuff including movement, perception, and mood.

You can think of serotonin as a hormone that is circulating around the brain and helps regulate behavior at a more global scale.

You can also think of serotonin as a neurotransmitter that is released from one cell to communicate with others.

In any event, serotonin can bind with many different types of serotonin receptors that are involved in regulating all of these behaviors, from mood to even making you hallucinate.

Once serotonin is released into synapses, it is taken back up by transporters to be used again and some is broken down by enzymes.

People vary in the amount of serotonin produced, the amount of receptors produced, the amount of transporters produced, and the amount of enzymes produced. Mental health problems can be related to any of these mechanisms, but our drugs tend to work on the transporters or the enzymes directly.