John Gill Commentary Psalms 44:3

"For they gat not the land in possession by their own sword, Neither did their own arm save them; But thy right hand, and thine arm, and the light of thy countenance, Because thou wast favorable unto them." — Psalms 44:3 (ASV)

For they got not the land in possession by their own sword ,
&c.] There were many things which show that the possession of the land of Canaan was not of the Israelites themselves, but of the Lord; as their passing over into it through Jordan as on dry land; the manner in which Jericho, the first city of it, was taken, and the smiting of the Israelites by the men of Ai;

neither did their own arm save them ;
from their enemies, and deliver them into their hands: they were too apt to ascribe things to their own righteousness, merit, and power; but such methods were taken by the Lord as to prevent such attributions to themselves; see (Deuteronomy 8:16Deuteronomy 8:17) (9:3-6) ;

but your right hand, and your arm, and the light of your countenance ;
the mighty power of God, his outstretched arm in their favour, and which arose from his pure good will to them;

because you had a favour unto them ;
was well pleased, and took delight in them; chose them to be a special people to himself, above all people on the face of the earth.