Fetching details from the dictionary...

to step into (e.g. someone else's territory); to break into; to raid
to come to grips with; to get to the core of
令状を持った警察が容疑者の家に踏み込んだ。
The police raided the house.
彼の私生活やプライバシーに踏み込むのは失礼だ。
Don't intrude into his private life.
表面的な議論ではなくもう一歩踏み込んで考えよう。
Let's think one step deeper.