What is dental stabilization?

Immobilization. Dental stabilization is the use of wires or adhesives to immobilize teeth so that they can reattach & become more stable. This is used to attempt to save a tooth/teeth.
Stabilization. Teeth are not like steel posts in concrete. They will shift and change over time. Dentists strive to minimize untoward movement. Trauma, loss of one or more teeth, pernicious habits, failure to wear post-orthodontic retainers as directed, and other factors, will all contribute to dental instability. Enhancing stability reduces need for reparative treatment.
TMJ Support Device. What you're referring to is a "stabilization appliance" = a type of oral appliance used to support & stabilize the jaw joints in people who have joint pain or associated muscle pain. There are different types of appliances used for this purpose, but they all hold the jaw in a comfortable & neutral position while preventing tooth-to-tooth contact caused by grinding/clenching. They're very helpful.
Stop movement. its a way to keep teeth from moving and shifting-- something that can, and does, happen throughout our lives.
? Are you asking about stabilizing the teeth after trauma that dislodges them from the sockets? If so, then this is just using dental wire or bonding materials to hold the teeth in place while the bone sockets heal.