The linear velocity refers to a distance traveled per unit of time. It is sometimes referred to as the tangential velocity for an object moving in a circle. The linear velocity (v) of any point on a rotating turntable is related to the angular velocity (ω) and the distance the object is from the axis of rotation (R). The equation relating these quantities is
v = ω*R.
For two points on the same turntable, the angular velocity (ω) is the same. So the point that has the largest R (is furthest from the axis of rotation) will have the greatest linear velocity (v).
One way to conceptualize this is to understand that each point is moving along a circular path as it rotates about its axis. But the point that is furthest from the axis moves in a circle with a larger radius and a larger circumference. Since each point makes a complete revolution in the same time (i.e., they have the same period and angular velocity), the one that must travel a lengthier pathway (larger circuference) is the one with the greatest linear velocity. And so the points that are furthest from the turntable's center are moving a larger distance in the same time and have the greatest v.