open the door for
1. Literally, to open a door for another person. Open the door for me, will you? I have my hands full right now. Now that I'm on crutches, I really appreciate it when people open the door for me.
2. To create an opportunity for someone or something. Female professors like you really opened the door for future generations of women scholars. Recent advancements in technology really opened the door for my latest invention to gain widespread acceptance.