The "first fruit" that is mentioned several times in the New Testament refers back to the offering of first fruit in the tabernacle, as specified in Leviticus 23:11 - "He is to wave the sheaf before the LORD so it will be accepted on your behalf" (NIV). Jesus today represents that offering to God. Of note is the fact that Jesus rose from the dead on the exact day of that sacrifice.

What it means to us today is the same thing it alwas has: Jesus is our perfect offering to God as a sacrifice for our sins.