1To come nearer; to draw close (in space or time).
電車が駅に近づくと、車内にアナウンスが流れた。
As the train approached the station, an announcement played inside.
台風が近づいているので、明日は外出を控えたほうがいい。
A typhoon is approaching, so it's best to avoid going out tomorrow.
試験の日が近づくと、どうしても緊張してしまう。
As the exam day draws near, I inevitably get nervous.
2To become acquainted with someone; to get closer to or grow familiar with them (emotionally or socially).
新しく来た同僚に近づいて、まず昼食に誘ってみた。
I approached the newly arrived colleague and first invited them to lunch.
彼女に近づくには、まず信頼関係を築くことが大切だ。
To get close to her, it's important to first build a relationship of trust.
その一件をきっかけに、二人は急速に近づいていった。
That incident led the two of them to grow close very quickly.