As the ices in the nucleus are heated and vaporized by the Sun, gas escapes, taking dust particles along with it. The brief trail that is seen is the material that has burned off and is still glowing as it cools.
Most meteors are only about the size of a grain of sand, and burn up completely in the atmosphere.
The duration and intensity of the shower is determined by the size and density of the cloud of dust. If the cloud is widely spread out, then the shower could be seen as a few meteors per hour for several days.