In general, 'reconstruction' is the practice of rebuilding something. This can be a crime-scene, a broken vase or any number of things. In Paganism, Reconstruction means the practice of reviving lost religious, social and practical practices from a specific time period or people. It is not that different from reconstructing a vase, actually, and I will be using that analogy a lot today.
Imagine this; long ago, a potter made a vase. He needed to make one because he had something which needed a holder. He shaped it in a specific form, inspired by his culture and need, and when the shape was done, he decorated it with imagery that was also culturally inspired. Somewhere over the years, the vase broke into a dozen pieces. There was no need for that particular vase anymore, so no one put it back together. Now, people need a holder again, and it seems logical to put the original holder back together instead of making a new one, because the first one functioned very well. They realize that in order to put the vase back together, they need to understand the culture and whatever was going on in the head of the potter who made it; without that knowledge, they won't be able to figure out how the pieces fit together and they can't restore the imagery without knowing what the potter created in the first place.
This is the basic idea of a religious Recon practice; religion was practiced, it got lost and now we try to piece together that ancient practice because we feel a need to revive it and serve the Gods in a way which They are familiar with. In order to do that, we need to look at the whole of the culture in which the religion was practiced. If we don't, we can't answer a lot of 'why' questions and we miss the nuances of the religious practice in its hay-day. In short, this is why I go on about slavery, hounds, children and other issues from ancient Hellenic culture; how the ancient Hellens thought about these issues was influenced by their culture and thus helped shape their religious practice. I need to know these things in order to practice my religion.
Recon practices are, of course, offset by other Pagan practices. To go back to the vase; practitioners of modern Pagan faiths saw the fragments of the vase, realized they could make such a thing as a vase but felt no need to make that vase to serve as a holder. They created their own from the many different fragments found, inspired by modern culture. This vase is as beautiful as the restored one, but there are a lot of differences between the two.
Anyone who wishes to adopt a Recon Tradition needs to realize that not only your practice changes, but your entire outlook on life and controversial issues might change as well. In most cases, adopting a Recon Tradition means leaving a part of your autonomy behind. You place yourself firmly under the rule of the Gods. They rule you and your life, so most of your day will be spent appeasing Them. You will do this with daily rituals, by including the Gods in every aspect of your life, by offering regular sacrifice, by abstaining from practices They frown upon and by striving to incorporate the qualities They hold in high regard into your own life and person.
Adopting a Recon practice means studying a lot. Not just about the Gods in your pantheon, but also about the people who worshipped these Gods first. What they strived to create in themselves and their society, are assumed to be the things the Gods value in modern day practitioners as well. By adopting the mindset of our religious ancestors, we strive to become better servants to the Gods. I realize that for many people, this submission to the Gods is hard to deal with. I see it in reactions I get from the community on this blog but also in reactions to the adoption of ancient practices which are controversial into general Paganism, like veiling.
I have always submitted to the Gods so the changes weren't that impressive, only the form changed. I have, however, become more aware of what I do, say and believe in. Miasma has become a major influence in my mental and practical religious life and, because my main shrine is in the bedroom area of our little home, I do worry about mooning the Gods on occasion. Other than that, though, I have no difficulties with a Recon faith. I still call myself a feminist while trying to copy the virtues of women in ancient Hellenic life. I still call on the Gods when I am in need of guidance but the form has changed. I still don't drink, do drugs or smoke. I was not forced to adopt any practice I can't stand behind; I understand why they matter and that is enough for me to adopt them.
Applying modern ethical or religious standpoints to the practices of the ancient Greeks is pointless; even modern Reconstruction has very little to do with these ethical and religious standpoints, although society-at-large is an influencing factor. Trying to sort out which practices to bring back and which to leave in the past is a subject which deserves its own post so allow me to save that for a future date. For now, let me end this post by saying that I greatly enjoy reconstructing my old vase. It's battered and missing some bits and pieces, but with every post, with every book I read, with every voice I hear, it becomes more complete. Hopefully the differences between Recon and non-Recon faiths have become a little bit clearer with this post. Honestly, I'm still trying to figure it out myself; it's all part of my vase.