# On that day

This phrase is used to talk about a future restoration between Israel and Yahweh.

# I will make a covenant for them

Yahweh's new covenant will include peace for the animals.

# I will drive away the bow, the sword, and the battle from the land, and I will make you lie down in safety

Yahweh will keep Israel's enemies away from them, there will be no more war, the people will be safe. Here "the bow, the sword, and the battle" represent war. 

# lie down in safety

This expression refers to living in safety.