This is a trait developing between two groups who are similar. They have a common ancestry, they descended from the same species. Let's say chickens and ducks came from the same ancestor. But for whatever reason they both evolve spots. Then dark stripes. Even though they split into separate species, their evolving in similar ways in response to the need for adaptation. Their phylogeny has them on separate branches, but still headed in the same direction, parallel.
Don't this confuse this with convergent evolution. Fish became streamlined to fit ocean life, and so did dolphins but while they both did the same thing, they didn't come from the same place. They don't have a very recent ancestry together, ones a mammal ones a fish.
Parallel applies to when their is a common ancestry the two species diverged from.