I was discussing my day at work with my family, and I had spent much of the day resolving conflicts after doing a merge of two divergent branches. Of course, neither my wife nor my son understood what I was talking about, so I came up with a very simple analogy to explain what I was doing.
Imagine a teacher wrote out a plot outline for a book, and then assigned each student to write one chapter. The student writing chapter 5 decides that the heroes need to use a shovel, so he make a small change in the draft of chapter 3 so that they find a shovel at the beach. Meanwhile the student writing chapter 3 decides she doesn't like the beach scene, so she changes it so that they go for a hike in the woods instead.
Eventually the students have to put all their work together. The conflicting changes demonstrate two types of conflicts:
First, in adding in the shovel in chapter 3, the first student made changes to a paragraph that the other student also modified in changing the scene from the beach to the woods. When using an automated merge tool, this sort of conflict is automatically detected, and the person doing the merge is shown the conflict.
Second, if in resolving the direct conflict, it's possible that the shovel is removed from chapter 3. The merge had been completed, but no automated tools will tell you that the shovel used in chapter 5 now comes out of nowhere. If this were computer code, this would either show up at compile time ("Error: Reference to undefined object "shovel" in chapter 5, paragraph 12."), or worse, would introduce a bug that only shows up when the code runs under certain circumstances. If the book merge left the shovel out, hopefully it would be found by the editor (testing by the quality assurance team for a software project), not left for readers to be confused by (a bug in the field).
The right analogy can often make it much easier to explain things. If you like this one, or have questions about other aspects of software engineering that you would like me to find similar analogies for, please comment.