I beseech you, brethren, (ye know the house of Stephanas, that it is the firstfruits of Achaia, and that they have addicted themselves to the ministry of the saints,)
First-fruits of Achaia - the first Achaean converts. Epenetus was the first convert of this "house," if the Received Text be right; but oldest manuscripts read Asia for Achaia in Romans 16:5. The image is from first-fruits offered to the Lord (Leviticus 23:10: cf. 1 Corinthians 15:20). This family was baptized by Paul himself (1 Corinthians 1:16).
Addicted (set) themselves to the ministry of (to) the saints - voluntarily (cf. 2 Corinthians 8:4).