To carry to extremes; to go to the end of something; to bring something to its limit or utmost degree.
彼は剣術を極めるために毎日稽古を続けた。
He practiced every day to perfect (master) his swordsmanship.
研究を極めて、その分野の第一人者になった。
He pursued his research to the utmost and became a leading authority in the field.
趣味を極めると、仕事にする人もいる。
When someone perfects a hobby, it sometimes becomes their profession.
To reach the peak of something (e.g., luxury or hardship); to be extremely (in the sense of reaching an extreme degree).
贅沢を極めた料理が並ぶ高級レストランだった。
It was a high-class restaurant serving food of extreme luxury.
彼の忙しさは極めている。今年は休む暇もないと言っていた。
His busyness is extreme — he said he has no time to rest this year.
To exhaust completely; to have nothing left (e.g., resources or strength are used up).
長時間の運動で彼は体力を極め、動けなくなった。
After long exercise he exhausted his strength and couldn't move.