To understand shutter speed, lets first understand what shutter is. In simple words, a shutter is a like a curtain (but not an actual piece of cloth of course) in front of the camera sensor which remains closed until you take a picture. In that brief moment when you hit the click button, this curtain rises and thus opening the camera sensor to the light that travels through the lens aperture. Once the sensor has recorded the light or in simpler words, formed the image, depending on the shutter speed selected, the shutter closes down again, stopping the light from reaching the sensor.
Likewise, simply put, Shutter speed defines the length of time a camera shutter remains open to allow light into the camera sensor.
For example, imagine an empty bucket under a water tap. Longer the faucet remains open, more the amount of water that will pass through and fill in the bucket. Same way, the longer the shutter remains open, more and more light will hit the sensor and get recorded as an image.