When a gutter fills, water goes over the front lip instead of down the spout. It runs down the fascia board, behind the gutter, into the soffit, and onto the soil packed against your foundation. Rotted fascia, stained siding, wet basements, and cracked walkways all start the same way.
Winter turns that from a maintenance issue into a damage issue. Standing water in a blocked gutter freezes at the roof edge, meltwater from the warm part of the roof backs up behind the ice, and it finds its way under the shingle course and into the framing. A cleanout that costs a couple hundred dollars prevents a repair that costs thousands.
Clogged gutters are also a pest invitation — standing sludge is where mosquitoes breed, and packed wet debris is where carpenter ants and squirrels get their start on your roof edge.