When a wave is formed in a pipe, it is a longitudinal wave.  In a longitudinal wave, the particles move in the same direction as the wave is travelling.   However, they do not themselves travel.  The energy is transferred because the particles vibrate causing other nearby particles to vibrate as well.

The picture above shows how the particles vibrate.   In a real wave, the wavefront moves as well.  This is how sound is transferred.  The picture below shows a wave moving left to right.

When we consider waves in pipes, we often use the length of the pipe (l) to calculate the wavelength of the wave created.   However, the wave does not end exactly at the end of the pipe.  You have to consider the end correction.  This is a small extra distance added to the pipe to make up for the effect that diffraction around the end of the pipe has.

See the Hard section for more information.