It's an aspect of japanese animation. There are many meanings behind it. First is that Danzo is elderly and the elderly japanese often have narrowed, wrinkled eye sockets. Second is that it is sometimes either a stereotype of a narrow-eyed trait. For example, Gin in Bleach spoke with an informal kyoto accent so they gave him eyes similar to those from Kyoto. Third is a character trait. Closed eyes also symbolize mystique, charisma and comedy in characters. Naruto himself kept his eyes closed for a large portion of the first half of the series. His is representative of a fox and thus parallels Kurama. It's more or less the same with Gin and Danzo, albeit it's a double edged sword with Gin because he also represented a snake. Ay even called danzo a sneaky old fox at the kage summit. When they open their eyes, it's like they are revealing their cloaked natures as it is a rare, unexpected thing and makes them come off as getting serious or fierce with the situation. Saito from Rurouni Kenshin possesses narrow eyes and when he first introduced himself, to help keep his nature and identity under wraps, he smiled and kept his eyes closed when he introduced himself. It creeped out and ticked Sanosuke off and he stated "your eyes are too narrow for my liking..." For this same reason, Ichigo could not read Gin's movements, personality, fighting style or feelings when they first met and it creeped him out as well, to which he called him a fox face, and later in the deicide arc stated he couldn't remember reading his heart.