What is wave interference?
Interference is when two or more waves from different sources are present at the same time in the same space to create a new wave. The more useful part of this question is what happens and what types there are...
when the compressions and the rarefactions match they create a wave of higher intensity.
When the waves are out of phase, as in the opposite to constructive interference but the sound is louder in some places and softer in other places. Often leading to pulses and beats of sound.
What is Phase?
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.
The relationship between the waves to form the new wave, often used to describe the resulting sound, commonly constructive or destructive.
This is where the compression of one wave matches or is in phase with the rarefaction of another and so the sound is cancelled out and nothing is heard.
What else to consider
Sound waves also change speed due to rarefaction from entering different mediums such as air to water, thus changing angle and bending the wave. this leads onto:
The critical angle
When a waves entering angle reaches a certain point it's called the critical angle. The rarefaction is parallel to the dividing line between the mediums. The greater the difference in speed from the sound in the two mediums, the greater the critical angle.
What does this mean?
If the sound hits the new medium with any angle smaller than the critical angle it will not be able to enter and so be reflected from the dividing line. Even if it enters the medium some will be reflected because of waves rarely propagate in straight lines only.
Example... A wave travelling through the air hits a building at 20 degrees, which for this example is less than the critical angle, then it is all reflected at 160 degrees as the total angle is 180 degrees of the wall. If the wave is above the critical angle then most will enter the brick and speed up because the molecules are closer and so is refracted. The rest bouncing off because it won't all be entering with in the critical angle.