Shutter Speed - Originally a term for film photography, the shutter speed was the amount of time the shutter of the camera was held open for in order to expose the film to the light. For digital photography and videography, the sensor is exposing constantly, so it's more akin to compositing layers.
A slow shutter speed will let in a lot of light, but also a lot of movement and therefor blur, depending on the level of movement of your subject of the camera operator.
A fast shutter won't let in much light, but little movement, so images will be sharper and fast motion can appear frozen in time.
Shutter Speed for Video
With video work, shutter speed cannot be adjusted for exposure without impacting natural motion blur, so it is generally left at around 1/50 or 1/60 (2X fps), double that of the standard 25/30fps for natural motion blur. This is what's known as the 180° Shutter Rule, a term derived from its origins in film cameras.
If your camera does not give you the option to adjust your shutter speed, the video recording settings are usually double the frame rate as above.
Whilst called a 'rule' consider it a guideline, as there are occasions where this could be adjusted for practical purposes, such as adjusting for flicker or banding from lights or screens, or for creative purposes, such as creating dream-like or high energy visuals.
An excellent article if you'd like more depth on the topic: 180 Degree Shutter