Except they aren't exactly particles in the way we think of particles at human scale. They also behave like little waves. This dual nature is common to the stuff you find at the subatomic level. It gives rise to phenomena that are sometimes non-intuitive. Diffraction is one of those phenomena.
Waves are able to reinforce and cancel one another.
If two troughs meet, the result is an extra-deep trough. Similarly, if a peak and a trough meet, they will cancel each other out, and the result is a flat spot. These rules about waves also apply to photons. When two photons have waves that reinforce each other, you get a brighter spot. When the waves cancel each other out because they coincide peak to trough, you get a darker spot.