Velocity is defined as the displacement divided by time, represented by the formula v = s/t. It measures how fast an object is moving in a specific direction, making it a vector quantity. Initial velocity refers to the speed of an object at the start of a time interval, while final velocity indicates its speed at the end of that interval. Displacement, on the other hand, is the shortest distance from the starting point to the final position. Understanding these concepts is crucial for grasping the fundamentals of motion in physics.