What is a backward compatible design?

The design is backward compatible, if the design continues to work with earlier versions of a language, program, code, or software. When the design is backward compatible, the signals or data that has to be changed does not break the existing code.
For instance, a (mythical) web designer decides he should make some changes, because the fun of using Javascript and Flash is more important (to his customers) than his backward compatible design. Or, alternatively, he decides, he has to make some changes because he doesn't have the resources to maintain multiple styles of backward compatible web design. Therefore, our mythical web designer's decision will inconvenience some users, because some of the earlier versions of Internet Explorer and Netscape will not display his web pages properly (as there are some serious improvements in the newer versions of Internet Explorer and Netscape that make the older versions of these browsers incompatible with, for example, DHTML). This is when we say, "Our (mythical) web designer's code fails to work with earlier versions of browser software, therefore his design is not backward compatible".
On the other hand, if the same mythical web designer decides that backward compatibility is more important than fun, or, if he decides that he does have the resources to maintain multiple styles of backward compatible code, then, obviously, no user will be inconvenienced when Microsoft or Netscape make some serious improvements in their web browsers. This is when we can say, "Our mythical web designer's design is backward compatible".