On this video, photographer Jay P. Morgan from the Slanted Lens looks at the different aspects which will help you control the freezing action of a shoot while considering the overall light of the image.
If you are not using an artificial light source and you are shooting outdoors in the sun all you need to do to stop the action in a shot is increase the shutter speed. However, if you are shooting when the ambient light is scarce and you need artificial lights to freeze the action things become a bit more complicated.
What you need to understand about a flash (or a strobe for that matter) is that they have a specific duration (it takes them a specific amount of time to reach full power and then they gradually stop). All of this happens very quickly of course
IGBT technology which Morgan talks about helps to cut down the flash duration even more (there are similar technologies going with different names from different brands). What you need to understand is that if you are using this technology you will get less light (as you are basically cutting the amount of light the flash/strobe produces). This will mean that you might need to increase the ISO.
If you are O.K. with a black background you can keep your shutter speed relatively high/fast but if you want to capture the background as well you will need to lower the shutter speed to get more light in (unless of course, you have a way to light the background as well with strobes). In this case, you might end up with some blurring in your shots (like Morgan got with the hands of his dancer).