Java is a full-featured programming language that has the special ability to run on multiple types of computers and inside web-pages. Programs running inside a web page are referred to as applets, because they are generally smaller than stand-alone applications such as Microsoft Word (everything is smaller than Word). Stand-alone applications can also be written in Java making it an excellent choice if you need a cross-platform applications or one that runs on a network (networking is a strong point of Java). Some java applications I like are Jedit, a great text editor, and Eclipse, a nice java IDE.
Here are some educational applest I've written to help my kids. KidMath is a math problem generator. Mad Adlibs makes crazy stories and Speller helps memorizing matching lists (like states-capitals) and their spelling. Reverser lets kids practice recognizing the correct orientation of numbers and letters, a common problem with beginning readers.
Here are a couple of applets I wrote for a class I took in 1997. Strings shows off Java's ability to manipulate words and characters. Color Picker gives the RGB (red green blue) numbers used by computers to specify colors. The Quizer applet displays a sequence of multiple-choice questions.