Noise is a scourge that has plagued many a photographer since the earliest days of digital photography. We've all experienced it. But that doesn't mean you have to live with it. And to cope as best you can with it, you need to start by understanding just what noise is and where it comes from.
Believe it or not, you already know all about noise, but may not realize your knowledge and experience of noise more broadly also pertain to your photography. Let's suppose you're talking with a friend. It's an interesting conversation. But just then, a group of other people enter the room carrying on their own conversation. But their conversation begins to take on a more boisterous nature, turning into an argument, or perhaps even a shouting match. It's hard to hear what your friend is saying with all that noise. Yes, noise. It's the same thing, but in an entirely different context. "Noise" here is a distracting pattern of sounds that makes it difficult for you to hear what you are trying to listen to. Noise in digital photography is a distracting pattern of data being fed to your camera sensor that makes it difficult to register the image data you are trying to capture.
It's impossible to get rid of all noise. Even in a laboratory anechoic chamber, there will be some background noise, but the level is low enough that you can barely, if at all, hear it unless you really try to. Noise in everyday circumstances is rarely more much of a distraction, but if you go to a big rock concert or sporting event, the sound can overpower everything else. And if your conversation instead happens to be while sitting in a crowded theater in the middle of a motion picture or symphony orchestra, you become their noise, making it hard for them to hear the performance.
At its core, it's a classic "signal to noise" problem. So long as what you're hearing being "louder than" the other inputs, you can make out what they're saying. If their words are getting drowned out, you can't. The more the other sounds fade into the background, the more clearly you can hear the words. As the noise level increases, it will eventually reach a point where it overwhelms everything else.
A similar situation exists when your camera sensor is trying to record an image. Generally, it can do the job it was built for pretty well. If it didn't, you'll get rid of it and find a better camera. But sometimes, the signal getting recorded by some of the pixels (photosites) has competition from other signals. In this case, it's noise coming from the simple fact that a camera, and specifically the image sensor within it, is an electronic device. And that can generate noise.
Most noise problems result from shooting under low light conditions. That won't inherently cause noise in and of itself, but in order to record a useable image with little available light, you'll need to adapt by either boosting the ISO setting significantly, or by keeping the shutter open a lot longer, and both of these can exacerbate noise. But in the end, if there isn't much light falling on the sensor while the shutter is open, the resulting signal will be low. And that makes it more likely to get drowned out by noise. Remember, your sensor is electronic, and it simply isn't possible for not do so at all. Maybe if you could cool your camera sensor to near absolute zero it might be almost theoretically possible, but seems unlikely on my budget and probably yours as well.
Sure, with money and a good enough engineering job, sensors that are less sensitive to noise can and do get invented. The first digital camera I bought last century created images that look like they were made with electronics from the last century. Surprise, things get better over time, or at least in this case they do. Other problems may get worse, but camera makers have definitely gotten a better over the years. If you're having a problem with digital noise and haven't bought a new camera in a few years, stop reading this and go buy one. It's OK, I'll wait till you get back after you tell your friends how I helped you solve your noise problem. If you can afford it, upgrade your camera, and your noise problems will likely be gone or at least made much more manageable.
But if that doesn't describe your particular situation, or you've already done so and are now back to complain that I still haven't solved your noise problem, don't give up hope. You can at least take some solace in knowing that sooner or later Nikon or Canon or whoever will come up with a better sensor and camera that should likely improve you whatever noise problem you may be encountering. But in the meantime, take a look at the ISO and shutter speeds you are using. If you can achieve the same exposure by lowering one and raising the other, try it. Some cameras are more susceptible to high-ISO noise while others have more of a problem with noise from prolonged exposure times. Do some tests under various conditions to help determine which variable you should be favoring when setting exposure for your next potentially problematic shot. There are also some techniques involving stacking a number of shots via software to combine the exposure from them all into a single image.
Some might be wondering if resolution affects noise. It's hard to generalize, but generally (sorry) neither one unduly affects the other. But what can have an affect is pixel density. At some point, you reach a point of diminishing returns through cramming more and more pixels into a small place. Light does travel in waves, and if the pixels approach the same order of magnitude in terms of size, it becomes increasingly difficult record an accurate value for all those pixels even under the best of light. This is why mobile phone cameras, who's sensors are likely no bigger than the thumbnail on your little finger, generally (sorry) have more problems shooting under low light than their bigger DSLR camera brethren do. And why full frame (Nikon FX) generally (sorry) have fewer noise problems than do the smaller APS-C (Nikon DX) sized sensors. All other things being equal, size does matter for camera sensors. If built during the same technology vintage, a bigger sensor should have larger pixels than a smaller sensor with an equivalent number of megapixels would. And with bigger targets, more light will be able to fall on each photosite during an equivalent exposure duration. And this means a stronger signal, to overwhelm whatever noise may be present.
But noise isn't new to digital photography. Back in the days of film, the same thing happened with the image being recorded by the film emulsion. We called it "grain," and it was an especially pernicious problem when shooting in low light or with faster speed films. It might also be fair to use the word "noise" to describe other forms of image degradation scenarios. Glare, for instance, makes it harder for your sensor to get an ideal signal. So too would a greasy fingerprint on the front element of your lens. See, everyone knows what noise is, even if it might go by a different name.