When you shoot still frames, you want them to be tack sharp. For that purpose, you set a fast shutter speed to prevent motion blur. In video, you want that little blur in the image. 

To get a smooth video, your shutter speed should be two times the frame rate. For example, if you shoot at 30 frames per second, you should set your shutter speed to 1/60s. If you want to shoot outside, in bright daylight and use a wide aperture, you will need neutral density filters to reduce the amount of light getting into the lens. If you get your shutter speed higher instead, you will get jagged videos.

Higher shutter speed can bu useful if you want to give a certain look to your video. Steven Spielberg used a fast shutter speed for the beach scenes at the start of Saving Private Ryan. It adds drama to the scene. It would not look that good in a wedding film. Once again, it is a basic rule that can be broken but do it for a reason better than being too lazy to put the neutral density filter on the lens.

On a side note, for the GH4 users, there is a better way to set it. In movie mode, if you go to page 6 of the camera menu, you sill see SS/Gain Operation. Set it to ANGLE/ISO instead of SEC/ISO. You can now set the shutter angle to 180°. That means that your shutter speed will always stay twice the frame rate. You don't need to bother with the shutter speed anymore. If you go from 24fps to 60fps (or use variable frame rate), the shutter speed will adjust automatically.