Code clones are sections of code that accomplish the same thing. Sometimes they are a result of copy and pasting or can occur when two or more people end up implementing some common functionality without realizing it.
Code clones become a problem when it is time to make a change to them. Can you remember every place where you've copied a code fragment? Most likely not (Juergens et al.) Once one fragment is found to have a bug, all clones of it likely also contain the same bug.
Further, knowing where code clones are gives you a chance to refactor some of that common functionality. Benefits of this are more than just maintenance costs of remembering where everything is, but also can improve the program size and runtime complexity allowing for further compiler optimizations.
Elmar Juergens, Florian Deissenboeck, Benjamin Hummel, and Stefan Wagner. "Do code clones matter?" http://dx.doi.org/10.1109/ICSE.2009.5070547