I found that most of KDE applications requires
libqt libraries. So, What is the relationship between KDE and QT?
QT is an application framework for various operating systems. Its probably most famous for creating graphical interfaces, but has libraries for other purposes, like multimedia or network functionality. You may want to read http://en.wikipedia.org/wiki/Qt_(software) for more details on QT.
KDE, is primarily a graphical desktop environment like Gnome or Xfce. However it also contains a wide range of applications that are (logically) not part of a desktop environment, e.g. an office suite, games and much more. All these programs utilize the core KDE libraries, which are used to display windows, grant network/file access, etc.
The point is, that these KDE libraries are not written from scratch, but are built on top of the QT libraries. Therefore, to put it in a nutshell, KDE is a desktop environment that depends on QT.