To become misty or hazy — used when visibility or a view is obscured by mist/fog (commonly written 霞む).
朝もやで山がかすんで見える。
The mountains look hazy in the morning mist.
遠くのビルが霞んで、形がはっきりしない。
The distant buildings are hazy and their shapes aren't clear.
春の霞で田んぼが淡く霞んでいる。
The rice fields are softly hazed by the spring mist.
To get blurry or grow dim — used for eyesight, images, or details becoming unclear (often written 翳む in some usages).
長時間の勉強で目がかすんできた。休憩しよう。
My eyes have started to blur after studying for a long time. Let's take a break.
古い写真は色が抜けて、全体がかすんで見える。
Old photos have faded and look washed out/blurred overall.
To be overshadowed or outshone — used figuratively when something becomes less conspicuous because something else is more prominent.
新人の活躍で彼の成績がかすんでしまった。
The newcomer's success has overshadowed his achievements.
母の料理は昔は特別だったが、最近は他の店が多くてかすんでいる。
My mother's cooking used to be special, but recently other restaurants have appeared and it has been overshadowed.