Digital Cameras always produce a certain amount of noise in their sensor signal. Whether this noise is visible depends on how much the camera has to amplify the sensor data (ISO-value), which again depends on how much light is entering the lens and how sensitive the sensor itself is. That’s why cheap, small cameras produce more noise than expensive cameras: they have larger, more sensitive sensors and usually better optics.
Scenario 1: I want to shoot at night, I have plenty of time, but only a relatively cheap camera. The object I take photos of does neither move nor change in any other way. I want a great image without noise.
Scenario 2: I have a great camera, but even when shooting with ISO 100 (Canon etc.) or 200 (Nikon), the image noise is visible because I only want to use a very small part of the tonal range (e.g. in foggy situations) and therefore the small amount of noise is heavily amplified.