High ISO capability refers to a camera's ability to deliver clean, as opposed to noisy, images at high ISOs. ISO is a number that represents a sensor's sensitivity to light, and while using a higher ISO brightens an image, it also diminishes images quality by introducing noise. A camera with good high ISO capability is able to use higher ISOs before image quality degrades to an unusable level.
High ISO Technical Explanation
Digital camera sensors use pixels, or photosites, to "collect" photons of light, and thereby create an image. The entire sensor has a single "base" or optimal light sensitivity, also known as its quantum efficiency. Quantum efficiency is, in simple terms, the sensor's efficiency at turning photons into electrons. In other words, when the pixels on a sensor are able to gather the most light they possibly can, this results in the best image quality possible for that sensor.
High ISO Performance
As light sources get dimmer, fewer photons hit each pixel. Thankfully, sensors can amplify the "image information" they do receive, thus rendering the resulting image sufficiently bright again.
Each ISO corresponds to a stop of light; ISO 100 is often where digital cameras "start", and ISO 200 is one stop brighter, ISO 400 is another stop brighter, and then ISO 800, 1600, 3200, 6400, 12800, ...and so on and so forth.
Technically however, the camera is not actually changing the sensitivity of the sensor itself. It is merely amplifying the existing signal, during the conversion process from an analog signal to a digital signal, before the image is actually created and written onto the memory card.
Both sensor design and the physical sensor size will affect the image quality of a sensor, especially when using a higher ISO. For each stop higher you set your ISO, a correct exposure will exhibit slightly more image noise, less sharp detail and color quality, and less overall dynamic range.
A larger sensor has an advantage, however, because each pixel is much larger and therefore collects more photons overall, both in individually and the sum total across the whole sensor. This is why a "full-frame" sensor is often preferable for photographers who highly value low-noise, high quality images even at high ISOs.
Smaller sensors, however, are also becoming highly efficient at "collecting photons", and therefore deliver good quality images even at commonly used high ISO's such as 1600 or 3200.
What is ISO "HI-1" or "H1"
At a certain point, a sensor's amplification capability becomes unreliable, and cannot achieve a precise "stop" that qualifies as a certain, specific ISO. At this point, the camera lists this as "ISO HI-1", to note that you will no longer be getting an accurate exposure. (Nor will you get very good image quality!)
Contrary to popular belief, however, "HI" ISO's do not always denote the exact point at which a camera switches from performing its gain amplification natively, (during the analog, photons-to-electrons conversion) to "fake" digital post-production brightening. For example, a camera may switch from analog gain to digital gain for ISO's higher than 3200, yet still list ISO 6400 before going to "HI".
What is Dual Gain ISO?
Some of the latest digital sensors tout having what is called "dual gain ISO". Dual gain is a technology used in sensors to change the amplification of a sensor's image data at an earlier stage in the analog-to-digital conversion. (ADC) It is still not an actual change in the quantum efficiency of the sensor, but merely a "cleaner" way to amplify the image data, which results in a slight boost in image quality when jumping from the next-lowest ISO. On most cameras which currently offer dual gain, this happens in the vicinity of ISO 400 or 800.
This does not mean that ISO 800 is higher quality than ISO 100, rather, ISO 800 is simply higher quality than ~1 of its preceding ISO values. This technology also results in consistently better image quality at all ISO's higher than that dual-gain switch point, compared to if that same sensor had kept using the original gain factor of its base ISO.
(NOTE: Apologies to the camera geeks out there for any gross over-simplifications! Please feel free to bring up any discussion on our Facebook group, for the benefit of all!)