This is the 8566th most frequent Japanese word.
捨てる
"To throw away" or "to discard."
Here, '捨てる' means physically disposing of an object, in this case, discarding an old chair.
その古い椅子を捨てることにしました。
I decided to throw away the old chair.
In this sentence, '捨てる' metaphorically conveys the idea of letting go of abstract concepts, such as past failures.
彼は過去の失敗を捨てて、前に進むことを選びました。
He chose to let go of past failures and move forward.
Here, '捨てられた' is the passive form of '捨てる' and refers to someone abandoning the kitten.