ISO is amplification. The sensor collects however many photons it collects; ISO decides how loudly that signal gets turned up before it becomes an image. ISO 100 is a whisper, ISO 6400 is a shout. Raising ISO does not gather more light — it just makes the light you gathered register brighter.
The cost is noise. Amplifying the signal also amplifies the random electrical fluctuation underneath it, which shows up as grain in shadows and colored speckle in flat areas. Every sensor has a point where noise stops being texture and starts being damage, and larger sensors generally reach that point later.
Modern cameras have made high ISO far more usable than it was a decade ago, and computational noise reduction has pushed it further. The working habit is still the same: keep ISO as low as the scene allows, raise it deliberately when the alternative is a blurry or unusable frame, and remember that a noisy sharp photo beats a clean smeared one.