Edit conflicts happen when two or more people try to edit a page at the same time. The most common occurrence is when Person A starts editing, then Person B starts editing, finishes, and saves the page before Person A. When Person A clicks "Save page" an edit conflict will occur.
When Edit conflicts do occur, a special edit page is generated, which consists of three parts. You can see an example of this to the right. Click on the image to enlarge. Edit conflicts have three main parts, detailed below.
Part 1: Edit Conflict
The first part of an edit conflict looks exactly like hitting the edit button for the first time, except it holds a warning that indicates that a conflict has occurred. In fact, that's pretty much what it is. The text displayed here is what is currently on the page, including all the edits since you last looked at it. Whatever is in this first Textbox is what will be saved to the page when you click "Save Page". This box shows the most recent of the page without any of the changes that you want to make. This is important to remember, as clicking "Save Page" without making any adjustments will cause all your changes to be lost.
Part 2: Differences
Following the Notices about editing and copyright is the "Differences" section. Two columns compare that page as it would have been with your edit, and the page as it currently is. Basically, it compares the Textboxes above and below, with the one below (your edits) shown on the left, and the one above (the page as it stands) shown on the right. It is a lot like viewing the differences between revisions in a page's history. This can help you find what you need to add to the top box in order to include your edit along with everyone else's, or to remove/change in the top box in order to resolve conflicting edits.
Part 3: Your Text
Finally, there are the the changes you had submitted. The text box provided is quite handy, since you can simply copy your changes and paste them into the top box; in most cases, this will require only minor editing.
Overcoming Edit Conflicts
The simplest way to overcome an edit conflict is to use the Differences section to determine what you need to change, if anything, in the top box in order to include your edits. When you are done, just click "Save Page". Remember: The wiki is here so everyone can contribute. It is important to make sure the edits before yours go unharmed.