The name "ISO" is the official logo of the International Organization for Standards. The French version of the name, Organisation internationale de normalisation, arranges the words in a different order for proper syntax in french. The letters "ISO" correspond to neither arrangement.
The three official languages of the ISO are English, French, and
Russian. The organization's logos in two of its official languages,
English and French, include the word ISO, and it is usually referred
to by this short-form name. The organization states that ISO is not an
acronym or initialism for the organization's full name in any official
language. Recognizing that its initials would be
different in different languages, the organization adopted ISO, based
on the Greek word isos (ἴσος, meaning equal), as the universal short
form of its name. However, one of the founding delegates, Willy
Kuert, recollected the original naming question with the comment: "I
recently read that the name ISO was chosen because 'iso' is a Greek
term meaning 'equal'. There was no mention of that in London!"
The ISO has written many technical standards, technical reports, technical specifications, etc. Each of these is assigned a number by the ISO. Three standards that apply to the sensitivity of photographic film are ISO 6, ISO 2240, and ISO 5800. Over time, a film's speed was referred to as its "ISO" because the number used to describe the film's speed was in compliance with these ISO standards.
With digital cameras, "ISO" has continued to be used as a way of expressing a digital camera's sensitivity to light at various amplification levels of the analog electrical signals coming from pixel sites on the camera's sensor. The International Organization for Standardization has released new standards for light sensitivity in digital sensors. In theory, an ISO setting of 400 on your digital camera should result in an exposure equivalent to one on ISO 400 film. Film sensitivities varied slightly from one film manufacturer to the next. A film that had an actual value of, for example, 388 based on the ISO standards would be marketed as "400 speed". Likewise, most digital cameras vary slightly at different ISO settings from the exact standard. At least one company, DxO, publishes test results for many cameras. If you go to the link and select the "measurements" tab you can see that the actual ISO can vary by as much as 1/2 a stop for the three entry level camera bodies I selected.
The primary thing regarding ISO you should be aware of when taking pictures is that, in general, the higher ISO number you select, the "noisier" your image will be.¹ Noise is an electrical signal from a pixel that was caused by anything other than light falling on it. When the signal from a sensor is amplified to increase ISO this noise is amplified as well. As your camera (or processing software on your computer) processes the signals from your sensor, certain measures are applied to smooth out the noise. Most cameras have settings that allow you to select how much noise reduction you want applied to the images you shoot. The downside to heavy use of noise reduction is that it also reduces the sharpness of the image at the pixel-to-pixel level. Because of this, it is best practice to shoot with the lowest ISO number that allows you to select the aperture and shutter speed combinations you desire. On the other hand, a blurry image due to a too slow shutter speed can't be fixed in processing. A noisy image that stopped the motion of your subject can be dealt with to a degree.
¹ This generalization is based on the assumption that as one increases the ISO settings, one decreases the amount of light allowed into the camera in order to avoid overexposing the highlights in the scene.