[Note: In this post, I use the terms "elder" and "elder-candidate" interchangeably.]
Elders, and elder-candidates, must be spiritual leaders in their own households. As Paul writes to Timothy, "If anyone does not know how to manage his own family [household], how can he take care of God's church?" (1 Timothy 3:5, TNIV).
Looking at the instructions about elders in 1 Timothy 3:2-5 in terms of "household responsibilities" provides a fresh perspective on how to understand these instructions. In the ancient world, the responsibility to lead and direct a household fell to the males, and, in particular, the father. Households included both males and females, children and slaves. The father was over all and responsible for moral instruction and making sure that members of his household did not bring disgrace upon the household. Fathers would rule their households by authority and discipline.
Paul gives attention to this cultural norm but also subverts it in his instructions to Timothy. He begins by stating that an overseer is to be "above reproach" (1 Tim. 3:2). This is the leading thought for the entirety of the instructions about elders; the remainder of the teaching (1 Tim. 3:2-7) describes what it means or how it looks to be "above reproach."
For good reason, the first block of teaching (there are three blocks, each detailing an area of character) is devoted to household relationships. Being above reproach means, first of all, leading one's family well.
But how is the elder to be above reproach in his family? He is to be "faithful to his wife" (1 Tim. 3:2). Here, the original language refers to a "one-woman-man." To translate it as "husband of one wife" is to interpret the phrase, and a better understanding of the phrase is seen in the TNIV, "faithful to his wife."
Thus, the elder is above reproach in his family by being faithful to his wife. Theologically, this carries more freight than the legal question about marital status. It recalls the Old Testament teaching about faithfulness to God and the covenant, seen, in particular in the prophetic book of Hosea, where faithfulness in marriage is a sign of faithfulness to the covenant.
But faithfulness in marriage contains a lot more than sexual faithfulness. This is clear by Paul's emphasis to Timothy that elders are to be "temperate, self-controlled, respectable, hospitable, able to teach, not given to drunkenness, not violent but gentle, not quarrelsome, not a lover of money" (1 Tim. 3:2-3). The key is to see these things evolving out of the elder's responsibilities to his household.
These instructions tie together Paul's teaching about faithfulness to one's wife within the household context by linking instructions about how the elder is to treat his wife with instructions about his children. The emphasis on "managing" the household in 3:4 is intentional. The word sometimes translated as "family" in 3:4-5 should be translated as "household." How an elder deals with the entirety of his household responsibilities is what's important. How he loves, leads, cares for, manages, and handles anything that comes up in the household, from relationships to business arrangements, pertains to his leadership of the church.
The principle is this: the household is a microcosm of the church, which is the macrocosm. Thus, "If anyone does not know how to manage his own [household], how can he take care of God's church?" (3:5) The character traits Paul lists in 3:2-5 pertain to oversight of the household.
We do not fully understand this passage when we appoint elders based on whether a man has been divorced and whether he has "good" kids. This passage teaches us to probe deeper, that we ought to get into an elder-candidate's life, to see how he really is around his family. We need to see how he loves his wife, how he treats his children, how he handles his finances, how he acts towards friends of his children, how he contributes to household chores and business. It's in these concrete and visible things that we see the true (spiritual) leadership of an elder.