Bioflavonoids are flavonoids from a biological source. Hence the "bio". Anyway, they are the same thing.
So, what are flavonoids? They are antioxidants. And antioxidants are good. You hear about it all the time. They are found in foods like dark chocolate, coffee, and other stuff. Bioflavonoids are found in a variety of foods as well and have a lot of benefits. Such as helping the body fight against allergens (things that cause allergies), viruses (things that make you sick), and carcinogens (things that cause cancer).