Found a hole in my exterior wall behind the gutter downspout. What caused this and how do I fix it?

That hole is usually a sign of water damage from a leaky or improperly sealed downspout, or possibly pest activity drawn by moisture. First, check the downspout itself for clogs, cracks, or loose connections where it meets the gutter and the wall. You need to identify the source of the water causing the damage. Water intrusion here can lead to rot in your wall framing, mold, and attract pests, making it a bigger, more costly problem if ignored. A licensed contractor needs to assess the extent of the damage to the sheathing and framing. Depending on the size and what they find, a permit may be required for structural or significant exterior repairs.