Pitch is the precise highness or lowness of a musical note. A singer can sing higher or lower pitches by raising his voice higher or lower, just as a pianist can play higher or lower pitches by playing higher or lower keys on the piano. If a note is sung at a pitch slightly off what is written in the music, that note is said to be off-pitch, off-key or out of tune. Notes sung off-pitch are not pleasant to listen to because they don't fit in with the rest of the music.
When you speak or sing, your vocal cords produce vibrations in your throat. Pitch is determined by the frequency of vibrations in that sound. The vocal cords vibrate faster when you produce higher-pitched sounds and slower for lower-pitched sounds. To feel pitch in action, try putting two fingers over your Adam's apple on your throat. First say your name, and then whisper it. You can feel vibrations when you speak but not when you whisper because your voice has a pitch, but whispers don't.
Professional singers must be able to sing on pitch, or their songs will sound discordant and wrong. To sing on pitch, you must take a deep, supported breath to carry your sound. Proper breathing is a skill in singing that produces proper tone and accurate pitch. You should also release vocal tension to sing on pitch -- that is, release physical tension in the throat and mouth when singing to let notes come more freely. Finally, it helps to have a good ear for pitch so you can tell if you are singing off-key and modify your singing.
Correct pitch is the foundation of music that's enjoyable to listen to. Music is structured in such a way that certain notes in a song sound pleasant when played together. If one note or phrase in a song is off-pitch, it will clash with the other notes, resulting in dissonant music that simply doesn't sound good. It's extremely important for singers to have a good sense of pitch and for music to be played or sung with correct pitches.