High ISO is a traditional expression from the film days. High ISO is 800 ASA and up. It's always been that way. When you reached the 800 ASA film, you were buying high ISO along with the attendant grain. You had to be much more careful with your exposure and your process.
In digital cameras, there's a specific phrase called expanded ISO which is accessible but not recommended ISO. After that it's up to the camera manufacturer to decide what ISO they stop recommending.
On full frame expanded ISO usually starts at 6400 ISO and up (some specific models like the Sony A7S family might consider expanded ISO above 51200 ISO but that's very high).
For APS-C, expanded ISO is also in the above 6400 ISO range now but previously began above 3200 ISO.
For Micro Four Thirds, those little sensors are noisy from 1600 ISO with expanded ISO beginning as low as 3200 ISO.
Expanded ISO is finally really moving up though. The Fujifilm APS-C sensors in the X-T2, X-T20 and X-H1 hold together right through 12800 ISO. Expanded ISO as it's camera specific is a moving target.
But as soon as you are at 800 ISO you are into high ISO. Just go and look at the charts for your camera (and other popular cameras) at DXOmark and see what happens when to dynamic range and signal to noise when you reach 800 ISO and above in comparison to 50, 100 or 200 ISO.
400 ISO is the last ISO where most digital camera images still look their best. The drop off in dynamic range is already two full stops by ISO 800 for the Sony A6300. Signal to noise for the A6300 has gone from 44.4 to 36.4, already out of DXOmark's green zone. Color sensitivity holds up better but is below optimal perceptible levels by ISO 3200.
I've been careful to pick good and representative cameras here: the Sony A6300, Panasonic DMC-G80 and Canon 5D Mark III are considered among best of class for their respective categories (APS-C, MFT, full frame) and are all have been extensively used by pros and semi-pros. Outliers like the Sony A7S series don't change the rule. High ISO is 800 ISO and above.
Personally I won't shoot my Sony NEX-5T above 800 ISO, my Canon 5D above 1600 ISO or my Canon 5D Mark III above 3200 ISO. On each camera the deterioration in image quality is too perceptible at that point. Even looking at the Sony A7S which is tuned for ISO, a usable picture continues to exist at much higher ISO (say to 51200) but a lot of life has gone out of its picture by ISO 6400 (at that point, Sony A7S dynamic range has fallen from 13 stops to 10 stops).
High ISO, IBIS (in body image stabilisation) and fast autofocus should not be a replacement for good photographic technique. Tripods, pre-focusing and slower exposures still play a huge role in creating high quality images.