Noise is unwanted sound on an electrical signal that when reproduced can be heard by the listener. White noise is random frequencies whereas a ground-loop hum can be around 50Hz or 60Hz. Other unwanted noise can include electromagnetic interference from other sources such as radio waves.
All analog electrical circuits and components generate noise and as a general rule, the more analog components you have in a signal chain the more background noise there will be. This is why some mixers allow you to 'bypass' sections of the mixer such as the EQ section.
The amount of background noise to the direct signal can be expressed as a ratio and this is called the signal-to-noise ration or SNR.