Hello Sam I am....nice name...you can tell I have children
Usually all that staining is mold.
Usually just cleaned up with some TSP cleaner(ask your hardware folks)or some bleach and water mix. And....lots of that ol' standby...elbow grease...so roll up those sleeves and get a scrubbin broom.
Basically it will show up on the shingles as run marks down the roof...then down the gutters and fascias.
Nothing to worry about.
Turn on the radio and have at it.