What exactly is the meaning of "Hu Tehilasecha"?
Ramban #2: It means that it is your association with Him that makes you praiseworthy (that raises you above) the other nations. 3
Seforno: 'Be proud to be an Eved of the One who rules over all existence'.
Mesilas Yesharim Perek 17: When serving Hashem, one must clean himself from seeking praise from people. His intent should be only towards our Master. He is all our good and perfection, and nothing other than Him.
What does "ve'Hu Elokecha" imply?
Ramban: It implies that He placed His Name upon you to be His people and that He will be for you a G-d, to offer you His personal protection, Because from the great and awesome deeds that He will perform on your behalf (Hashgachah K'lalis - communal Providence) 1 you will realize that you are His lot and His inheritance, and that His Eyes are always upon you to do good to you.