A menstrual cup is a feminine hygiene product, used during your period. It is a small, flexible funnel-shaped device made of rubber or silicone that you insert into your vagina to collect and hold menstrual blood. The "disc" is a variation of the cup (kind of like a diaphragm with a pouch attached).
Cups (and discs) can hold more blood than other methods, leading many women to use them as an eco-friendly alternative to tampons. And depending on your flow, you might be able to wear a cup for up to 12 hours (4-12 hours is typical). This can help you sleep through the night on a heavy flow day.