When a gutter becomes blocked the water builds up and overflows onto your external wall, a common cause of overflowing gutters is fallen leaves, vegetation growth and even birds nests blocking parts of the gutters and preventing rainwater from travelling to the downpipes.
This can lead to walls becoming saturated, which in turn leads to wet rot issues, mould and damp issues, frost damage, erosion of the pointing and ultimately increases the porosity of the wall.