# Then it sprouted

"Then the seed began to grow into a plant"

# a spreading vine low to the ground

"a vine that spreads out on the ground"

# Its branches turned toward him

The branches of the vine turned toward the eagle. This means that they began to grow upward towards the sky.

# its roots grew under it

Possible meanings are 1) "its roots grew under itself into the ground" or "the roots of the vine grew under the eagle."

# So it became a vine

"That is how the vine grew"

# produced branches and sent out shoots

"grew branches and spread its shoots"