Noise   
(1) 
a random signal which contains all of the frequencies in the audio spectrum. 

white noise contains these frequencies equally distributed throughout the spectrum, 

pink noise contains equal energy per octave. pink noise, therefore has approximately 9/10ths of its energy in the 9 octaves between 20 - 10,000 Hz while white noise has only half of its energy in this portion. 

 (2) Subjectively speaking noise is unwanted sound. It is the sound that appeared in the mix that we didn't want to be there. 

It is often the result of distortion of the signal due to clipping or improper connections or the result of the operating noise of the electronic circuitry of the equipment being used. 

 (3) 
random activity of electrons - i.e. all audio systems have a noise floor or basic level of such activity.
 
Two kinds of noise are intentionally generated and used for a variety of purposes such as sound sources for electroacoustic composition and sound reinforcement setup and calibration. These are white noise and pink noise. See links for pink noise & white noise sound examples
 
  noise
 
White noise is the result of a random signal which contains all frequencies at varying levels. 

This is the same noise heard in electronic devices and is the result of random movements of electrons in the components of those devices as a result of heat. 

One of the characteristics of white noise is the perception that it is louder in the high frequency regions. This is because white noise has equal amounts of energy per hertz. This is a result of the fact that with each octave increase in frequency there is a corresponding doubling of frequency. This also results in a doubling in the range of frequencies available between octaves. 

Consider the range of frequencies in the octave described by 100 to 200 hertz compared to that of the octave described by 5000 to 10000 hertz. Clearly the second octave has a much greater range of frequencies. Consequently white noise, because it has equal energy at all frequencies, exhibits a 3 db per octave rise in level over its range of frequencies. 

 Pink noise is the result of a white noise signal being rolled off by a 3 db per octave low pass filter with a start point at a sub-audio frequency. This results is a noise which has equal energy per octave. 

Because pink noise is more balanced in its levels over a wide frequency range it is useful in testing and calibrating audio equipment which must perform equally well over the range of audible frequencies.