1To scratch or rub the surface of the skin with one's nails or fingertips, e.g. to relieve an itch (transitive). Usually written in kana.
蚊に刺されたところがかゆくて、ついかいてしまった。
The mosquito bite was so itchy that I ended up scratching it.
子犬が後ろ足で耳をかいている。
The puppy is scratching its ear with a hind leg.
背中がかゆいけれど、手が届かなくて自分ではかけない。
My back itches, but I can't reach it to scratch it myself.
彼は頭をかきながら、答えに困っているようだった。
Scratching his head, he seemed at a loss for an answer.
2To sweat; to perspire. Most often used in the set phrase 汗をかく (transitive).
夏の昼間に外を歩くと、すぐに汗をかく。
Walking outside in the middle of a summer day, you start sweating right away.
緊張のあまり、手のひらにびっしょり汗をかいた。
I was so nervous that my palms got drenched in sweat.
たくさん汗をかいたら、こまめに水分を取ったほうがいい。
When you sweat a lot, it's better to drink fluids frequently.
3To scoop, shovel, or rake away snow, earth, etc.; also to push water aside with the hands or an oar to move forward, as in swimming or rowing.
朝早く起きて、玄関前の雪をかいた。
I got up early and shoveled the snow in front of the entrance.
両手で水をかいて、少しずつ前に進んだ。
Stroking the water with both hands, I moved forward little by little.