Very small telescopes, including binoculars, can be hand held. However even very small telescopes and binoculars will show a lot of shake if hand held. Because of this telescopes are often mounted in some fashion in order to steady the image and often to allow the object to be tracked, compensating for the Earth's rotation.
Types of Mounts
There are many different types of telescope mounts, though these types do tend to fall into a few broad categories. Fixed, transit, alt-azimuth, equatorial with some other rarer types.
A telescope on a fixed mount is immobile and is permanently pointing in one direction (usually up at the zenith). These telescopes can be made quite large but can only observe a limited part of the sky.
The alt-azimuth mount allows the telescope the freedom to move in two axes and thus can look at any part of the sky. With proper computer control these mounts can also track an object.
The equatorial mount has it's rotational axis parallel to the rotational axis of the Earth. Thus equatorial mounts can compensate for the Earth's rotation by simply rotating about this parallel (polar) axis at the rate of the Earth's rotation (sidereal rate).
Other types of telescope mount include the alt-alt mount where both telescope axes are a change in altitude.