What is Turning points; bound and free motion?

For a conservative one-dimensional motion of energy $E_m$, the particle can only be where $E_p(x) \leq E_m$ (since $E_k \geq 0$); the points where $E_p = E_m$ are turning points, where the velocity vanishes and reverses. Trapped between two turning points in a potential well, the motion is bound and periodic; able to reach infinity, it is free; a potential barrier higher than $E_m$ cannot be crossed.