A
progressive wave is one where the
waveform travels, as opposed to a
standing wave (or
stationary wave) where the waveform is fixed in place. Most familiar
waves are usually progressive: light, sound, and water transmit energy along their direction of travel, though it is possible to set up standing waves for each of these. A plucked
string fixed at both ends vibrates in a standing wave though the musical sound it generates is a progressive wave.
Progressive waves, despite the name, can travel backwards as well as forwards. A standing wave is equivalent to two equal and opposite progressive waves.
It can be either a transverse wave or a longitudinal wave, depending on which direction the vibrations go compared to the direction of travel of the wavefront. The wavefront represents the pattern that is moving along. Each point along the path alternately becomes crest and trough of the wave, and each point has the same amplitude, that is it reaches the maximum extent of anywhere in the wave when it's at the crest. Contrast this with a standing wave, where some points (antinodes) are permanently at the largest displacement or intensity and some (nodes) are permanently at zero.
Also, a progressive wave has each point out of phase with its neighbours. When one is at a crest, others nearby are advancing towards the crest or falling away from it. Contrast again with a standing wave, where when the wave reaches its maximum amplitude, each point is at its own amplitude.