A true binary star is a double star system that consists of a pair of stars that are gravitationally linked such that both stars are in orbit around their common centre of mass. Over half the stars in the sky are part of a binary star system.
Other stars might appear to be binaries, due to a line of sight effect even though they are not gravitationally bound. These are known as visual or optical doubles and are not true binaries.
A system of three gravitationally bound stars is known as a trinary star, ternary star or a triple star. A quadruple star is a system of four gravitationally bound stars, while systems with more than four stars are generally known as multiple stars.
Mizar and Alcor in the constellation Ursa Major are an example of a double star that can be visually recognised as two separate stars if you have good eyesight.
Although Mizar and Alcor move together, as members of the Ursa Major Moving Group, it has yet to be demonstrated conclusively that they are gravitationally bound. However, through a small telescope, Mizar can also be resolved as a double. In fact, Mizar is actually a quadruple system and Alcor is a binary, making a six-star system.
Stars can also be gravitationally bound to neutron stars or black holes. Binary black holes also exist, which can sometimes coalesce to form a single black hole giving off huge amounts of energy as well as gravitational waves, which were detected for the first time in 2016. See starparty.com/gravitational-waves-detected/
Note that a type Ia supernova is a supernova that occurs when a white dwarf in a binary system accretes material from its companion star causing it to explode.
See also Star Clusters.