Noise is an electronic artifact - basically coloured speckles most visible in dark areas, and at high ISO. It's especially noticeable in pictures from mobile phones because of their tiny sensor size - they just don't gather much light to work with. Smaller the format, the worse the noise - all other things being equal.
Noise is always present but at a very low level. Normally it isn't noticeable because the image signal is so much higher it is effectively suppressed.
But when the light is low or the ISO is high, the signal-to-noise ratio is much lower and when the image data is amplified to get a nice good bright picture, so noise is amplified with it.
There are vaious ways to reduce noise, both in camera and in post processing. Most of them are very effective but all have their (slight) downsides.