Particles are a graphical effect in Minecraft. Particles always seem to face the player and will usually disappear after a short period of time. They only appear from another entity such as fire. Particles collide with solid blocks and are slowed by cobwebs, but are unaffected by other entities. Each particle texture is 8x8 pixels.
You can reduce the amount of particles visible in the Options menu. These options range from "All" to "Minimal". "All" renders all particles, "Decreased" renders half the amount of particles, and "Minimal" only renders block breaking particles, explosion particles, and firework particles.
Issues relating to "Particles" are maintained on the bug tracker. Report issues there.
Trivia
Most particle colors can be changed using resource packs, however the color of smoke particles used in redstone, portals, and Endermen can't be changed without mods.
The rain particles affect the rain sound.
Mobs spawned using a Monster Spawner emit smoke particles when spawning.
Status effect particles will appear where your face is pointing.
Bubble particles seem to only appear when they are in water.
Gallery
This is a picture of the render radius of particles. It seems to be round, but not entirely circular, as seen at the back.
An image of particles.png with the primary purposes of each particle texture explained.