1 Corinthians 16:15 (ESV)

15 Now I urge you, brothers you know that the household of Stephanas were the first converts in Achaia, and that they have devoted themselves to the service of the saints

Stephanas and his household belonged to a small group of Corinthians who had been baptized by Paul himself (1 Corinthians 1:14–16). Here Paul refers to them as the first converts in Achaia. Literally he writes that they are firstfruits of Achaia. The image of firstfruits was also used in 1 Corinthians 15:20 and 1 Corinthians 15:23. There, as here, it indicated a promising beginning that was given by God and that signified that more was on the way. 

In the absence of formally appointed elders (see comments under 1 Corinthians 5:3), the household of Stephanas have devoted (or appointed) themselves as leaders in the church. Paul describes their leadership in a positive way, as service of the saints (saints being a description of all the church members).