letter, writing brush
翰 centers on the tools and products of writing: a brush used to write, and by extension a letter or written document. The bird-related kun readings reflect an older association with feathers used for brushes.
翰 originally referred to a type of pheasant or bird with long feathers, and later came to mean a writing brush made from such feathers, and by extension a letter. The modern form combines 羽 (feathers) with a phonetic element on the left.
The right side is 羽 (feathers), and the left side looks like a person 十 holding a brush over a document 日. Picture someone using a feathered brush to write a letter.
For カン, imagine a can of ink next to the feathered brush: can -> カン, and you dip the brush into the can to write a letter.