Higher speed in photography can mean a few things, but usually the sensitivity or shutter speed. Higher ISO numbers are more sensitive, so ISO 200 needs half the shutter speed compared to ISO 100 for any given aperture. ISO 400 is twice as fast as ISO 200, so four times the speed of ISO 100. Raising the ISO allows you to use faster shutter speeds for the same exposure, but the trade-off is moisier images. Similarly if you open up the aperture buy a full stop, say from f/8 to f/5.6 you can then use a shutter speed twice as fast for the same exposure but the trade-off is shallower depth of field.
"Fast lenses" are ones which allow you to select low f numbers, usually f/2.8 and lower, corresponding to larger apertures which therefore allow more light to enter which allows faster shutter speeds for the same ambient light. The trade-off in this case being shallow DoF again, plus the fact that fast zooms are usually VERY expensive. Fast prime lenses (fixed focal length, no zoom) can be quite affordable though
As a rough guide, you want to be using shutter speeds of 1/200th or faster if you're trying to freeze fast human motion, and higher still for things that move even faster. Increasing ISO speed is often the only way to achieve this if the light is not great. I'd suggest putting your camera in shutter priority auto with ISO set to auto adjust, picking a fairly fast shutter speed such as 1/200th and taking some shots then checking what ISO the camera chose to get an idea of how high you need to go.