"May your home be open wide, may the poor be members of your household" means that the gate of your courtyard facing your house is to be open in such a way that the poor seem to be inside your home, to make it easier for you to go towards them and give to them yourself. This is a greater good deed that sending a messenger. Comfort them with encouraging words, for those who do so are blessed with eleven additional blessings, which is not the case when a messenger is used… This is how the Torah's verses in the Re'eh weekly reading portion should be understood: "You must open your hand and lend him sufficient for whatever he needs… which is why I command you: open your hand to the poor and needy kinsman in your land." One might ask why the words "open you hand" are repeated in the two verses… this may indicate that despite your courtyard gate being open, you should open yet another door, in such a way that the doorways face your dwelling-place, so that you may actually see the poor and give to them from your own hand, and not send a messenger, which is why it says - by way of emphasis - "your hand".