Spherical
A spherical mirror is a piece of mirror that's cut out of a reflective sphere. Essentially, a ball with a mirror on the inside or outside of it would be a spherical mirror. The bit used in a telescope would be bowl-shaped. A concave spherical mirror will reflect light from inside the bowl of the mirror. This shape condenses the large image so that it fits in the eye-piece for you to view.
Parabolic
Parabolic mirrors are made to capture energy or light and focus it to a specific point, which would be the lens you look through. Parabolic mirrors can cause images that are not in the center of focus to distort. That means that any bit of the night sky you are viewing that doesn't land directly on the center of the parabolic mirror will appear stretched out. The farther from the center of focus, the wider the image will appear.
Hyperbolic
A hyperbolic mirror is like a sphere, except the reflected side is on the outside of the ball. The ball can gather entire rooms into its field of reflection and make them look round and small. Unlike regular mirrors, which reflect images that are the reverse of what they appear, the hyperbolic mirror in a telescope reflects light back toward the viewer so that it is not inverted. They also gather a lot of light, such as in the night sky, and bring it to your eye.