Bringing along; accompanied by — the te-form of 連れる used when taking/bringing someone or something along.
週末は子供を連れて公園へ行った。
I took the children to the park on the weekend.
彼は彼女を連れてパーティーに現れた。
He showed up at the party with his girlfriend.
犬を連れて散歩するのが日課だ。
Walking the dog is my daily routine.
母を病院に連れて行った。
I took my mother to the hospital.
As; in proportion to — used in the pattern '〜に連れて' to mean that something changes together with another change.
年を取るに連れて体力が落ちてきた。
As I got older, my physical strength declined.
経済が発展するに連れて生活様式も変わった。
As the economy developed, lifestyles also changed.
経験を積むに連れて自信がついてきた。
As I gained experience, I became more confident.