It comes from the roof
Moss grows on roof tiles, especially on shaded or north-facing roofs. Rain washes clumps of it down into the gutter.
Why it blocks gutters
Moss is spongy. It packs together, holds water and traps silt and leaves, so it is often the start of a blockage.
Dealing with it
Clearing and washing the gutters removes the moss already there. If your roof is very mossy, expect to need gutter cleaning more often.