“Shutter speed” indicates for how long light will enter your camera and actually create the picture (on film or digital sensor). Fast shutter speed for instance might be a thousandth of a second (1/1000), just letting light in for very little time while show shutter speed might be half a second (1/2), letting light in for much longer.
How does it affect photo quality? Three ways:
The first one is quite obvious: if you shoot a picture with a still subject (e.g. an apple on a table) that does not move, you may shoot on slow motion with no or little blur. Conversely, if you shoot fast action (e.g. an athlete running) and want to freeze the action, you need to shoot with fast shutter speed. Otherwise, the moving athlete would be blurred. The faster shutter speed, the less blur. Generally speaking, one tends to prefer crisp pictures to blurred ones.
The second one is a little trickier. Let’s start with the technical aspect: the faster you shoot, the wider the aperture, thus minimizing the depth of field. To move away from optics and physics, it could be summarized as the faster you shoot, the less ‘depth’ you get in your picture.
The third one is linked to the opening statement: since shutter speed controls how long light gets in, shutter speed influences on getting dark or light pictures. To the extreme, shooting too fast would give under-exposed pictures, while shooting too slow would give over-exposed ones.
Because photography is at the edge between the science of light and the art of writing with this light, there is no ‘good’ or ‘bad’ answer. This is all about what YOU want to achieve. Blurred pictures might be superb, rendering movement, feelings … getting away from visible details. Pictures with shallow depth are very soft and very nice. Under and over-exposed pictures might also be very artistic. The ultimate difference is whether this was achieved by design or by accident.
Practice a lot. Try to get away from the standards. Fail many times, until you identify what suits you best.