Simply put, you tell us what you want your character to do (your orders), and we send back to you, based on those orders, what happened (your results). Perhaps that's an over-simplification, but it does describe the basic mechanic involved. This exchange is called a "turn."
Naturally, the game system requires that the orders be presented to us in a certain format. The way this works you the player fill out forms detailing what you want a character to do each turn. We then feed those orders into our computer programs which then create the results we send back to you. The cycle continues as you send in new orders based on the results you receive.
These games do not depend on fancy graphics and mindless destruction. They involve reading, thinking, decision making and most importantly, imagination.
Long, long ago, way back before the internet became what it is today, these type of games were called play-by-mail (or pbm for short) because that pretty well described how they worked. Once email became prevalent, some of the pbms became, at least partially, pbem (play-by-email) games.
The popularity of the world wide web has complicated things a bit as well - play-by-email no longer seems like an accurate name. We at Entertainment Plus have come to call these games "turn-based" because that seems now to pretty well describe how they work.
For Adventurers Guild, a turn occurs in a two week cycle. Once you are playing a game, you will find the deadline for order submissions for the next turn either in your results or in the newsletter. You have until that deadline to get your orders to us.
Once we have processed everyones orders and created the turn newsletter we send out the results. AG results are typically sent out on Thursdays.