Visual effects such as fire, rain, or smoke have one thing in common: they have a continuously changing nature and cannot be meaningfully described using a single sprite. Even an animated sprite is too limited for many cases, because such effects should come with certain randomness. Fire may have sparks flying in arbitrary directions; smoke may be blown away by the wind.
This is why we need another model to visualize these sorts of effects: particles. A particle is a tiny object that makes up a part of the whole effect; you can imagine it as a small sprite. Each particle by itself looks boring, only in combination do they lead to an emergent visual pattern such as fire.
A particle system is a component that manages the behavior of many particles to form the desired effect. Emitters continuously create new particles and add them to the system. Affectors affect existing particles with respect to motion, fade-out, scaling, and many other properties.
Given a particle texture...