Wikipedia says a 3-way merge is less error-prone than a 2-way merge, and often times doesn't need user intervention. Why is this the case?
An example where a 3-way merge succeeds and a 2-way merge fails would be helpful.
Say you and your friend both checked out a file, and made some changes to it. You removed a line at the beginning, and your friend added a line at the end. Then he committed his file, and you need to merge his changes into your copy.
If you were doing a two-way merge (in other words, a diff), the tool could compare the two files, and see that the first and last lines are different. But how would it know what to do with the differences? Should the merged version include the first line? Should it include the last line?
With a three-way merge, it can compare the two files, but it can also compare each of them against the original copy (before either of you changed it). So it can see that you removed the first line, and that your friend added the last line. And it can use that information to produce the merged version.