To Step Into
To Step Hard On, To Intrude, To Delve Into
godan verb
踏む is "to step on" and the kanji 込 means into, so this means to step into.
踏み込む means to step further and harder than usual, like stepping forward to lunge for a ball or stepping hard on the accelerator. Figuratively, it can also mean to intrude or to delve into, like stepping into someone's house without permission or exploring complex topics one step further.
The readings come from the word 踏む and the kanji 込, put together.
ルームメートが、私のプライバシーに踏み込みすぎだと思うのよね。
I think my roommate invades my privacy too much.