# He has made my mouth like a sharp sword

"He has made my words as effective as a sharp sword" 

# he hid me in the shadow of his hand

Yahweh protecting his servant and keeping his purpose secret is spoken of as if Yahweh's hand cast a shadow over him. 

# he has made me into a polished arrow; in his quiver he has hidden me

Yahweh's servant being able to carry out Yahweh's purposes effectively is spoken of as if the servant were a sharp, new arrow. 

# in his quiver he has hidden me

Yahweh protecting his servant and keeping his purpose secret is spoken of as if Yahweh kept him hidden in a case used to carry arrows.