1 Timothy presents the church as the "household of God." This is meant to be helpful parallel to the households of each person's family. As in any household, there are proper and appropriate roles for everyone. More than this, though, 1 Timothy believes that people who are recognized as being exemplary in their family households should likely be the leaders in the church. They handle their affairs honorably and well, they know how to manage finances and cultural expectations; having gained people's respect in the wider community, they have respect in the church. This also means that the roles of women are limited in the church; they can do no more than they can do in the wider culture.
According to this letter, there are some basic leadership positions in the church -- minister (who in this letter is Timothy himself), bishop (a sort of chairman/treasurer), deacons (both men and women who perform a variety of functions), elders (who were ordained and evidently paid), and widows (women who performed certain roles in the congregation in return for financial support. It is the minister's role to provide sound teaching, so that only people who should have such leadership positions are named to them.