The shutter controls how long the exposure is made for – its a time based control. You can let light hit the sensor for a very short amount of time – a fast shutter speed – or for a long time – a slow shutter speed.
Most shutter speeds are measured in terms of fractions of a second – 1/60th, 1/200th, etc. The normal progression of shutter speeds, in one stop increments is:
1, 1/2, 1/4, 1/8, 1/15, 1/30, 1/60, 1/125, 1/250, 1/500, 1/1000, and so on.
Some electronic film cameras have 1/2 stop and 1/3 stop shutter increments, and most digital cameras have 1/2 and 1/3 stop or even finer increments.
Its not unusual though to use shutter speeds in the order of seconds, and in extreme cases, minutes – this is definitely tripod territory. Also experimentation is required, as you need to see how your film or sensor will handle these long exposures.
With film you can suffer whats called reciprocity failure (or more accurately, the failure of the reciprocity law). This is where one stop more exposure gives you less than one stop of density on the film, so you actually have to expose for longer. With digital sensors you can suffer excessive noise on long exposures. The better the sensor, the less the noise.