ISO sensitivity, image noise and noise reduction are the topics here. First, noise – what exactly is it, what does it look like. Noise reduction can remove it, but often a photo just looks like it has been messed up in some other way afterwards.
Noise in digital photography means that pixels have random fluctuations in brightness and colour. It has several causes, at this point it is about the correlation with ISO sensitivity.
A higher ISO sensitivity leads to higher image noise. You can compare it to recording sound; if you record a quiet sound and then turn up the volume when you play it back, you also amplify distracting background noise and noise signals. High ISO sensitivities mean that signals from your camera's image sensor are amplified more strongly, so this comparison is quite fitting.
On the right a small section of a practically noise-free image with ISO 100 and below the same section, taken with very high ISO sensitivity. Both are very small sections, reproduced in 100%, so 1 pixel of the photo = 1 pixel here on the screen.
At which ISO sensitivities the noise increases and how much depends on the camera, that's why I've been avoiding the precise specification so far. Cameras have improved a lot over the years and sensor size also plays a role. So I'm not giving a concrete indication here at what sensitivity the noise is how noticeable, it may very well be different on your camera. But for the sake of completeness, they were taken with a Nikon Z6 II, a full-frame camera released in 2020, and the shots are exposed at ISO 100 and 25600, 8 stops of exposure difference.
If you have a choice, you are on the safe side for best quality with the lowest possible ISO sensitivity. Simple. But please don't be too stingy with increasing the ISO sensitivity:
Try it out on your camera, don't be frightened to push the possible ISO sensitivities and check the results.
Noise can be removed after the shot. Every camera uses noise reduction when it produces JPG files, just to varying degrees. In doing so, the image quality can suffer in that the undoubtedly lower noise image looks spongier and blurrier. Here is a section of the image with high ISO sensitivity from above, but with the camera's automatic noise reduction.
If you don't intervene in the camera settings yourself, your camera will probably automatically apply noise reduction. Then JPG files straight from the camera at high sensitivities will look more like this, not like the noisy image above.
Here is another section from three different shots that nicely illustrates noise and noise reduction:
Noise reduction is highly dependent on the software used. You can achieve even better results if you send RAW files from the camera through a good piece of software. And even the small smartphones do a remarkable job here and can compensate to some extent for their disadvantages due to small sensors.
When comparing noise, it is tempting to look at images in high magnification, as in my examples. BUT: Doing so you may well overestimate the noise. The small images above were displayed at 100% size; when a photo is displayed smaller, several pixels in the image can be combined into one on the screen, thereby reducing the visible noise.
So here is a comparison of the sample photos used at the very beginning, with ISO 100 and ISO 25600 - now the full photos and both scaled to 2000 pixels wide for display on the web. The original pictures from the camera were 6000 pixels wide, so ISO 25600 has the chance to catch up quite well by merging pixels... compare yourself, please in large size, by clicking on the pictures. I think the impression of the very high ISO sensitivity has improved a lot compared to the high magnifications before.
Just to be on the safe side, once again: please don't apply the results 1:1 to your camera, ISO 25600 will be more noisy on older models and smaller sensors. My point is to send the message that noise should not only be compared with a magnifying glass and that it is less visible in a reduced image size.
After all the preamble, here is a series comparing how the noise develops at different ISO sensitivities; taken with the same Nikon Z6 II as above and in the small sections with 100% display size.
Actual noise varies with camera models, mainly the sensor size. A camera with small sensor may have significantly higher noise at the same ISO sensitivity.
Please consider it as an illustration of how the noise increases slowly at first and then more and more clearly, not as an aid to reading off specific ISO sensitivities for your camera.