Shutter speed and frame rate are two terms that relate to both filmmaking and photography.
Shutter speed is depicted as a fraction such a 1/50th or 1/200th and relates to the duration of time the camera sensor is exposed to light. 1/50th means that the sensor was exposed for 1/50th of a second, whilst 1/200th means the sensor was exposed for 1/200th of a second.
Therefore the higher the shutter speed, the shorter the time the sensor is exposed. In photography, if you want to freeze motion such as water droplets or a sporting event, you need to shoot at a high shutter speed.
In filmmaker, shutter speed isn't commonly used, instead we use the term shutter angle which is depicted in degrees as opposed to a fraction. The most common shutter angle in filmmaking is 180° which means that the sensor is exposed for 50% of a frame where one full frame is equal to 360°.
Where as shutter speed represents the length of time one frame is exposed, frame rate represents the number of total frames in a second. The most common frame rate in PAL locations, such as the UK and Europe, is 25 frames per second (fps). In NTSC locations, such as North America, the most common frame rate is 24 or 30fps.
To film in slow motion you need to record a higher number of frames, such as 100fps, and then playback the frames at a slower frame rate.
For example, you record someone jumping at 100fps. The jump lasts 1 second, so you have 100 frames. To see the video is slow motion you playback the 100 frames at 25fps. Now your 1 second video clip of someone jumping lasts 4 seconds as the video plays back at 0.25x real time.