Caring for others

The earth and all its inhabitants are God's, but Torah says that we are something special. If we live in covenant with God, then we are God's סְגֻלָּה / segulah -- precious possession or treasure; we are מַמְלֶכֶת כֹּהֲנִים וְגוֹי קָדוֹ / mamlechet kohanim v'goy kadosh -- a kingdom of priests and a holy nation.

What can we make of this, and how does this relate to the story of Yitro with which the parsha began?