That's called a double star.
Moons orbit planets. Planets orbit stars. Some stars orbit other stars, or orbit their mutual center of gravity. Stars orbit the center of the galaxy. Galaxies may orbit the center of the "galactic group".
Gravity keeps the planets in orbit around the sun and the stars and the stars in orbit around the center of the galaxy. Gravity also holds the stars together against their own internal pressure.
They orbit as stars would in any other halo. It is gravity that causes everything to orbit and "spin around" Stars can also orbit around other stars called a binary orbit.
The stars are said to be a "gravitational binary pair"
Because stars have a greater amount of gravity
Double stars, also called binary stars, are valuable to astronomers because they are the only stars of which astronomers can easily calculate their mass. They are bound to each other by gravity and orbit about a common center. The time it takes for one star to orbit the other depends on the distance between the two stars and their masses.
The gravity of the entire Milky Way galaxy causes all the stars to orbit the center of the galaxy. Our Sun, with the whole solar system, takes about 220 million years to make one complete orbit.
Gravity! If the Sun (and all other stars and objects in the Milky Way) didn't orbit the center, they would eventually fall in to the central super-massive black hole at the center of the Milky Way.
Stars travel in various ways. On the largest scale, the universe expands, and stars move away from each other. On smaller scales, stars are most often part of galaxies and they orbit the center of the galaxy, while the galaxies themselves often are in orbit around a center of gravity of a galactic cluster.
A Binary star system A system of stars orbiting a common center of gravity where there is no mass at the center of gravity is known as a Kepler Rosette. Such an arrangement is theoretically possible but is unstable. No such an arrangement has (yet) been observed in the real universe. All objects in a Kepler Rosette have to have identical mass and exactly the same kind of orbit (differing only in their phase angle) and must be evenly spaced on some multiple value of their phase angle. If the orbit of such a Rosette is eccentric then the system will pulsate in diameter on the period of the orbit.
Plants don't orbit anything - planets do.
Typically one, like ours. But it is possible to have binary or even trinary star systems as well, where the stars orbit each other, and the other objects in the system orbit the center of gravity between them.