It is important to always read such verses in context rather than trying to pull out a meaning that could be different from how this verse was meant to be read. Especially in such Books of the Bible as letters, we must remember that the letters had a structure and a general argument, and each verse plays a part in the overall structure.
If we look at the general passage in which this verse occurs, it is entitled "Overseers and Deacons," and Paul in this section of the letter is outlining the kind of qualities that people should have in order to become an overseer or a deacon. Your own character is always your own best witness, and thus Paul recommends that such people wanting to receive a position of authority in the early church should not be drunkards, should be able to manage their money wisely and so on. Your verse comes as part of this list, and thus we can see the importance of how you manage your family. If you want to be in a position of ledership, your family should be able to indicate that you can manage people, after all. Note what the next verse says:
(If anyone does not know how to manage his own family, how can he take care of God's church?)
Thus it is that managing your own family is a very important characteristic if you want to gain a position of importance in the church itself.