If you've ever read an article about young stars, or seen an image of a star forming region, you've probably come across talk of disks around stars. Stars form from giant disks of material slowly falling, or accreting, onto them, so we expect to see disks around young stars. There are many different types of disks, and what you call the disk depends on the age of the star, the disk structure, and other properties of the system. Below are some definitions of different types of disks so you will understand what astronomers are referring to.
Circumstellar Disk: A generic term used to describe a disk of gas, dust, and rocky material around a young star. Most of the following disks are specific types of circumstellar disks.
Accretion Disk: A disk of gaseous material that spinning around and falling onto the young star. Often the inner portion of a circumstellar disk. Accretion disks can exist around other objects as well, such as black holes.
Protoplanetary Disk: A disk around a star that has aged ~3 million years or more containing mostly dust particles and rocks. This is the type of disks that planets form from.
Transition Disk: A slang term for a circumstellar disk around a young star that has a clear hole between the star and the edge of the disk. This occurs, for example, when a large planet forms and clears out a small portion of the disk.
Circumbinary Disk: A disk of material around a binary star system (two stars gravitationally bound to each other.) The disk surrounds both stars at once as if they were one object.
Debris Disk: A disk of material around an older star of any type. If a star begins burning Hydrogen in its core and still has a disk around it, it's called a debris disk. Also, a disk around a neutron star or a white dwarf would be referred to as a debris disk. These may occur from interactions with nearby stars, catastrophic collisions between planets in a system, or after the star dies and explodes.
Infrared image of a circumbinary disk around GG-Tau, taken with Gemini in Hawaii. The two stars are where the star symbols are (their light is blocked out on purpose) and the blue/white is the disk of material.
Image Credit: Gemini Observatory/AURA