I've never heard of that problem before (and this page appears very quickly when searching for it), but I'd be interested to see a link if you have one…
Ballasts turn DC (Direct Current) power from a mains supply, and convert it into AC (Alternating Current) power for the lamp, while also controlling the flow of power to the lamp. Not exactly sure what would happen if you didn't use a ballast, but I suspect you'd either have no light or a broken lamp. I wouldn't recommend doing any ballast modifications unless you know what you're doing.
Flicker is… well, this graph is the waveform of AC power:
(x-axis is time, y-axis is current/voltage)
As the current rises and falls, so does the brightness of a lamp. Have you ever looked at a tungsten bulb as it's turned off, and noticed it glowing for a moment while it has no power? The brightness in fluorescent lamps tends to decay much faster, so the flicker you see with your eye is often a cheap ballast is failing to regulate the current correctly, leading to the lamp dimming noticeably between waves.
When it comes to cameras, you see flicker when the camera's shutter is not moving in sync with the sine wave of an AC power supply. Each time the shutter opens and a frame is recorded, the lamp has reached a different point in the wave and so the quantity of light rapidly goes up and down. Flicker is usually avoidable by selecting a shutter speed that matches the frequency of the mains power supply - 1/50 or 1/100 in Europe, and 1/60 or 1/120 in the USA - so that every time the shutter opens, the lamp is at the same point in the wave.
(Take all of the above with a pinch of salt… my electrical knowledge is a bit patchy.)