1To step into or enter (physically) — e.g. entering someone else's territory or breaking into a place; to raid or force entry.
警察が容疑者の家に踏み込んで家宅捜索を行った。
The police broke into the suspect’s house and conducted a search.
他人のプライベートな問題に踏み込むのは良くない。
It's not good to intrude into someone else's private matters.
敵の領地に踏み込む決意を固めた。
They resolved to step into (invade) the enemy's territory.
2To come to grips with an issue; to tackle or get to the core of a matter (figurative: to delve into a subject).
その議論は具体的な費用の問題にまで踏み込んだ。
That discussion went so far as to get into the concrete cost issues.
教師は生徒の悩みに踏み込んで相談に乗った。
The teacher stepped in and took up the students' concerns in consultation.