Like the others have said, ISO is the digital equivalent to Film Speed.
With Film, ISO 64 or 100 were ideal for color. ISO 400 was considered high speed and could be "Pushed" to 800.
In extreme conditions like sporting events, ISO 800 could be Pushed to 1600. "Pushed" is a dark room technique used to double the film speed however, it caused a grainy affect. Of course the higher ISO allowed faster shutter speeds and/or a higher F/Stop. Black & White film always showed less grain.
With Digital, many factors determine high ISO image quality. The main factor is the size of the digital sensor. In DSLR cameras, you see the term "Full Frame". Full frame sensors have the same dimensions as 35mm film or 24mm x 36mm. Smaller sensors are considered "Crop". Full frame sensors give a wider view through the lens. In Nikon DSLR, FX is full frame, DX is Cropped and will give a zoom affect with the same lens. Full Frame will always have the better quality image and less Grain or Noise at higher ISO. With a top of the line Nikon DSLR like a D6, I'm not afraid to use ISO 6400.
Grain is a film term, Noise is more of a digital term. Noise is seen as a lack of color or details in a pixel. Noise is directly related to the size of the pixel / resolution of the sensor.
Resolution is the number of pixels. A sensor that is 4,000 x 3,000 pixels is a 12 MP sensor.
4,000 x 3,000 = 12,000,000 = 12 megapixels .
The number of pixels in the image is directly related to the size you can print. Most digital printers and print services consider 360 pixels per inch as photo quality. Divide the resolution by 360 and it will give the size of the available print. I minimum is 150 pixels per inch.
4,000 pixels / 360 pixels per inch = 11 inches
Pixels are different than dots per inch. Pixels are use to measure resolution in sensors, TVs, and monitors. Dots per inch are the number of ink dots a printer can produce.
Noise can also be caused when you edit the image. Sharpening is the most common cause of noise in editing.
With software like Photoshop, research a technique call "High Pass Filter Sharpening". This technique is the best I've found for sharpening without introducing noise. You can create a Photoshop Action that records your steps and reduce the time it takes. Play the Action and it will repeat the steps.
In DJI Drones, the sensor is measured in Video standards. A 1" sensor will have more resolution and less noise than a 2/3 sensor.