What does 'High Frequency' or 'HF' mean in lighting, tubes or bulbs?

It means when you look at the light you don't see flicker caused by the power-supply into your building.

With old-style fluorescent lighting and cheap LED-bulbs the mains 'AC' or 'Alternating Current' flicker-rate can affect your concentration and possibly even your health.

Even though the mains-power in the UK is flickering/alternating at up to 60-times per second, in lighting this is believed to be slow enough for your eyes and brain to notice and try to compensate for.
When you look at bright sun your eyes quickly adjust to reduce the amount of light entering, but if you try to do that 60-times a second some people experience headaches or eye-strain, and nobody likes it much.

LEDs and fluorescent tubes aren't just connected directly to the mains. Fluorescent and LED lighting relies on an attached controller that takes electrical power and converts it into the right spec of electrical energy to run the light-source. In fluorescent lighting this is usually still called the 'ballast'. In LED lights it's called the 'driver'.
However old fluorescent lights which had 'starters' make the tube flicker with the mains 'AC' rate.
What's more shocking is that some cheap LED-bulbs don't have components to prevent this mains 'AC' flicker. One health-related UK government department we supply tested LED-lights from another (previous) supplier and found they flicker too slow for good health of the staff working below them. Ours passed their test because we made sure they flickered so fast that the human eye/brain is not aware or affected (our LED downlights flickered approx 100,000 time each second!).

www.energyatwork.co.uk