One of the questions I am asked most frequently by students is: "What does each pedal do?". I try my best to explain the functions in person, but to complement my explanations here is a post detailing the piano pedals, their use, and application.
Most students have upright pianos at their disposal at home. Upright pianos rarely have an effectual "soft pedal". A teacher will explain to a student to a student, "The pedal on the far left is the soft pedal. Hold it down with your left and then when you play you should hear a muted sound with a different character." The student goes home, tries it, but alas the soft pedal produces no audible change. But the teacher has not lied. It's just that most upright piano soft pedals have no effect. They are just window dressing, garnish for the look of the instrument.
Also, upright pianos rarely have a functional "sostenuto pedal". Instruction regarding this pedal is also difficult for teachers, as often they work in their studio with a grand piano at their disposal and teach in light of that instrument and its capabilities. This can produce confusion for the student.
[Another source of confusion is this: many modern upright pianos are built with an extra soft pedal occupying the middle position of the three. This extra soft pedal can be pressed down with the foot and locked to the left, producing an extremely muted tone from the instrument.
What typically happens inside the piano when this pedal is applied is this: a long banner of felt or thin cloth descends between the hammers and the strings inside the piano, creating a buffer between the hammers' striking of the strings and thus producing a softer sound when keys are pressed.
This extra soft pedal is a modern innovation. One doesn't encounter it on older upright pianos, and I personally have never encountered it on a grand piano.]
Many students have as their home instrument an electronic keyboard or digital piano. These "pianos" typically have only one pedal (if they come supplied with any at all), a "damper pedal". Regardless of the instrument, the damper pedal is by far the most commonly used pedal. It is arguable that one could live their entire life loving music and playing the piano without ever bothering about the soft pedal or sostenuto pedal. Those two are employed mostly in advanced piano music, and even then satisfactory performances can be delivered without their use.
With all of the above out of my system, here are some informative links about each pedal, archived at the vast Virginia Tech Multimedia Music Dictionary website: