To make something cold or chill it — to lower the temperature of food, drink, or an object (refrigerate/cool).
ジュースを冷やしてから飲んだ方がおいしい。
It's tastier to drink the juice after chilling it.
傷は氷で冷やしてから病院へ行ったほうがいい。
You should cool the wound with ice before going to the hospital.
ビールを冷やしてパーティーに持っていった。
I chilled beers and brought them to the party.
To calm down, cool off, or cause someone to regain composure (to make calmer or less excited).
彼に言い返す前に一度頭を冷やしてから話した方がいい。
Before answering him back, it's better to cool your head and then talk.
試合で興奮しすぎた選手をコーチがベンチで冷やした。
The coach calmed down the player who got too excited during the match on the bench.
まず深呼吸して気持ちを冷やそう。
First take a deep breath and calm yourself down.
To frighten or to give someone a chill of fear — to cause someone to be scared.
暗い路地の足音が彼女を冷やした。
The footsteps in the dark alley sent a chill through her.
あの話を聞いて背筋が冷やされた。
Hearing that story gave me chills (it frightened me).