Polysomnography is the full overnight sleep study done in a sleep lab. Sensors record brain waves, eye movement, muscle activity, breathing effort and airflow, blood oxygen, and heart rhythm while you sleep, so a specialist can see exactly what happens through each sleep stage. It's the gold-standard test for obstructive sleep apnea and for other sleep disorders; a simpler home sleep apnea test is often used first when apnea is the main question.
For someone on a GLP-1 it matters in two directions: untreated apnea works against weight loss and recovery, and one GLP-1 medication is now approved to treat apnea itself — so a study can both open a treatment pathway and, later, confirm whether apnea has resolved as weight comes off. See the guide on getting a sleep study.