We say that a wave reflects when it is turned back at the edge of a medium.
The edge of the medium may be fixed, that is, the edge may not be free to move. Or the edge of the medium may be free to move, in which case it is often called an open end.
We will imagine a wave pulse traveling down a linear medium such as an elastic rope. The following two animations demonstrate how the phase of the wave pulse is affected upon the reflection of the wave.