أهلا صديقي
(Hello, Friend!)
Both prior posts are accurate and I'd like to add some from another point of view. These are what I'd call, "positional" descriptions, or "theological." There is, however, the practical aspect to consider, also. For me and my family, "conservative," is a way we interpret scripture and how it applies to our daily life. I DO NOT insist that all my brothers and sister of the faith see things the same, it is, to the best of our ability, the way we see God the Father leading us.
For example, my wife and daughters only wear dresses at all times. We don't disdain our Christian sisters who do otherwise, but this is a way in which we take a "conservative" view on ladies attire. By the way, we men, (me and my son,) dress in a conservative way, also.
My wife and girls wear the Christian sisters head covering as described in 1 Corinthians chapter 11, kind of like you do.
We are careful about the kind of entertainment media that comes into our home, like music, video, etc. Because we want to live our lives in a "conservative" manner, we want to re-enforce that lifestyle with things that support that view.
We believe in large families, (as large as God permits with wisdom,) and wives/moms staying at home, and homeschooling the children. We teach our children instead of having the "State" do it with their philosophies that we GREATLY disagree with.
So you see, "conservative" has different ways of manifesting itself in the lives of bible-believers.
Bro. Ben