To scratch (with nails or fingernails); to scrape or rub a surface (transitive).
蚊に刺されたところをかかないでください。
Please don't scratch the spot where the mosquito bit you.
猫がソファの布地をかいて穴を開けてしまった。
The cat scratched the sofa fabric and made a hole.
背中がかゆくて自分ではかけなかった。
My back itched and I couldn't scratch it myself.
To perspire; to sweat (often used in the phrase 汗をかく).
夏は外で作業するとすぐに汗をかく。
In summer, you start sweating quickly when working outside.
緊張して手に汗をかいた。
I got sweaty palms from being nervous.
To shovel or scoop (e.g., snow); to paddle or push with a tool (to move by scooping/paddling).
雪をかいて車を出した。
I shoveled the snow and got the car out.
川で櫂をかいて船を進めた。
We paddled the boat along the river with oars.