This is the 402nd most frequent Hebrew word.
מבלי
"Without" or "lest."
In this sentence, "מבלי" connects the act of not knocking to the main action of entering, specifying a condition under which the action takes place.
הוא נכנס לבית מבלי לדפוק על הדלת.
He entered the house without knocking on the door.
Here, "מבלי" introduces an action that is not performed relative to the main action described in the sentence, indicating the manner in which the main action occurs.
מבלי להפסיק לחשוב, הוא המשיך ללכת.
Without stopping thinking, he continued walking.
Here, "מבלי" expresses an inability to perform one action without the execution of another, adding a conditional dependency.