ISO is the digital equivalent (or approximation) of film speed. If you remember buying film for a regular camera, you’d get 100 or 200 for outdoors and 400 or 800 for indoors. The faster the film speed the more sensitive it is to light. All of this still applies to digital photography, but it’s called an ISO rating instead.
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The advantage of a low ISO is that the light in a given exposure is more accurately represented. If you’ve seen photos at night, the lights often look like they’re much brighter and bleeding into other areas of the photo. This is the result of a high ISO—a greater sensitivity to light. High ISOs are particularly useful for picking up more detail in a dark photograph without reducing the shutter speed or widening the aperture more than you want to, but it comes at a cost. In addition to lights being overly and unrealistically bright in your photos, high ISO settings are the biggest contributors to photographic noise. High-end cameras will pick up less noise at higher ISOs than low-end cameras, but the rule is always the same: the higher you increase your ISO, the more noise you get.
Most cameras will set the ISO automatically, even in manual mode. Generally you can stick with the same ISO setting if your lighting situation doesn’t change, so it’s good to get used to setting it yourself. That said, sometimes lighting changes enough in dark, indoor settings that letting the camera set it for you automatically can be helpful—even when shooting manually.