From the manpage.. "dialog" is a program that will let you to present a variety of questions or display messages using dialog boxes from a shell script. It just allows you to build a curses type interface to your shell scripts with simple commands.

Let's Play

display a messagebox dialog

dialog --msgbox "You are using dialog" 9 50

display a yes/no dialog and echo the resulting selection (0=yes, 1=no)

dialog --yesno "Do you like curses-style interfaces?" 6 50; echo $?

"xdialog" is a drop in replacement for "dialog". This means that the programs take the same command line parameters which makes it very simple to have your scripts detect whether they can show a graphical interface or a curses interface. We see this in this script.

Other programs exist that are drop in replacements (or very close) for the dialog style command set. Some are: whiptail, zenity, kdialog.. There are probably many more.

Links
A good dialog/xdialog Hands-On Tutorial