Rashi (from Tanchuma Bamidbar 3): A Yisrael knows that Hashem has the ability. If his prayer is not fulfilled, he knows that it is due to himself and his sin. A Nochri (if his prayer is not fulfilled, he) will complain and say 'the house whose fame goes from one end of the world to another, I exerted to travel greatly until I came and prayed in it, and I did not find Mamash (real power) in it, just like there is not Mamash in idolatry.

Rashi: If you see that a Yisrael will harm another with his money, do not give to him.

Radak: It is so all nations will know Your name, and know that Your name is called on this house. Amidst this they will know to fear You, like Your nation Yisrael.

Malbim: (a) The Nochrim will see that Hashem heeds lower beings and is close to all who call to Him, and their fear will come to resemble that of Yisrael. Yisrael's fear came through recognizing that Hashem oversees details which amazing Hashgachah. (b) They will know that Hashem's name is called on the house, and it is the gate of Shamayim.