A constant vector is defined as one that does not change in magnitude or direction as a specific variable, such as time, varies. It is important to note that a vector can have a constant length but still change direction, which disqualifies it from being a constant vector. For example, an object moving in a circle at a constant speed experiences acceleration due to the change in direction. Thus, the key characteristic of a constant vector is its unchanging nature in both magnitude and direction. Understanding these definitions is crucial for discussions in physics and mathematics.