In fluorescence, an object absorbs and releases lower energy light almost simultaneously, but in phosphorescence, the release of light is delayed. Both fluorescence and phosphorescence are types of photoluminescence.
The difference in the time before light is emitted in fluorescence and phosphorescence can be explained by looking at the electronic processes involved. What happens in fluorescence is that when an orbital electron of an atom goes back to its ground state after being excited to a higher quantum state, it emits a photon of light. This occurs in a matter of milliseconds. In phosphorescence, the excitation to a higher state involves a change in the electron spin state. Because of this, the electrons cannot easily relax back to the ground state. This process can take minutes or hours.
A classic example of phosphorescent materials are objects that glow in the dark. When placed in a bright room, these items charge up for a while and then glow when moved to a dark location, and then the glowing objects would cease emitting light after some time. An example of fluorescence can be seen when using a black light. Certain objects glow immediately, but only when the black light is shining on them.