To Arrange
To Organize, To Sort
When you arrange something with reason you're arranging it. That's why this is to arrange.
せいりする
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
本だなを整理してくれたこと、大変感謝しています。
I really appreciate that you organized the bookshelf.
この書るいを全て整理するには、大変な時間と労力が必要である。
It takes a great deal of time and effort to arrange all of these documents.
ちょっと話を整理させてね。つまり、男の人が浮気をするのはいいけど、女の人がするのはだめってこと？それがあなたの言いたいこと？
So let me get this straight. It’s okay for men to cheat, but not for women. Is that what you’re trying to say?