# to give us

The word "us" refers to James and his audience.

# give us birth

God, who brought us eternal life, is spoken of as if he had given us birth.

# the word of truth

Possible meanings are 1) "the message about the truth" or 2) "the true message."

# so that we would be a kind of firstfruits

"so that we would be like an offering of firstfruits"