Shutter speed is the amount of time the sensor inside the camera is exposed to daylight. It is measured in seconds or fractions of a second, and times vary depending on what you set it to.
When pictures are completely frozen in time, they use a higher shutter speed, and that lets daylight in for that amount of time, for example if I had a 1/250 shutter speed, the sensor would let in daylight for 250th of a second (extremely fast!) and therefore that makes the picture completely frozen in time, Whereas If I had a shutter speed of 1/4 of second, the sensor is letting in a whole quarter of a second (significantly slower than a 250th of a second!) therefore you can see the movement in the picture because the sensor has been exposed to daylight for much longer.
My Examples of Shutter Speed:
This image uses a Shutter Speed of 1/250. The picture is frozen in time and we see that he is frozen in mid-air. This is because the shutter speed is at 1/250 and therefore the sensor is exposed to daylight for 250th of a second therefore the picture is frozen in time and there is no movement.
This image uses a Shutter Speed of 1/4. We can see the movement in the picture because of the shutter speed is set to a quarter of a second. Therefore the sensor is exposed to daylight for much longer and that shows us the movement in the photo.