Javascript is a scripting language which is interpreted by web browsers (Internet Explorer, Safari, Firefox, ...)

JavaScript can also be used in applications outside web pages--for example in PDF-documents, site-specific browsers and desktop widgets, but it's most common use is in web pages.

Object-oriented Language:
Javascript is an object-oriented language. The object-oriented programming (OOP) is a programming paradigm uses "objects" - data structures consisting of properties (data fields e.g. color) and methods (program code - something an object can do) together with their interactions.

For example a circle object could have:
properties: x,y coordinates of the center and r -radius
   methods: Area - Calculate the area
            draw - print a circle with the properties in the object

DOM - Document Object Model:

Web pages use HTML (Hypertext Markup Language) to tell browsers how to display the information (text, graphics) and what to do with links or other objects.
Each HTML document loaded into a browser window becomes a Document object. It may contain things like Link Objects, style objects, button objects, form objects, ...
See: JavaScript and HTML DOM Reference at w3schools.com
and JavaScript - W3C DOM - Introduction at QuirkSmode.org

Standards:
Javascript has been standardized by the European Computer Manufacturers Association (ECMA) and is sometimes called ECMAScript.
Most browsers ( Internet Explorer [IE] 5.5 and above, all version of Firefox & crome, Safari 3 and above and opera 6 and above) support the ECMA version 1.5. Microsoft has their own version called JScript.
Firefox 4 supports up to version 1.8.5.
JScript is Microsoft's version which has additional features. See msdn.microsoft.com/en-us/library/hbxc2t98.aspx
See ECMAScript Versions at wikipedia

Libraries:
Many standard javascript functions are available on the internet for download. The most popular one is jQuery, with several books written on it.
jQuery is a fast and concise JavaScript Library that simplifies HTML document traversing, event handling, animating, and Ajax interactions for rapid web development. jQuery is designed to change the way that you write JavaScript (jquery.com). There is a free license for non-commercial projects available from MIT or GNU.

Java is different from javascript. It is a programming language originally developed by James Gosling at Sun Microsystems (which is now a subsidiary of Oracle Corporation) that can be compiled into machine independent byte-code programs that can run on a web server or applets which are downloaded to a web browser and run on a Java Virtual Machine (JVM).

JavaScript copies many names and naming conventions from Java, but the two languages are otherwise unrelated and have very different semantics.

Simple Examples:

OnMouseOver is a function built into browsers.
When you put your mouse over "onMouseOver" above it will display a comment
at the bottom of your screen.
e.g.
onMouseOver="window.status='MouseOver function';return true;" 
onMouseOut="window.status='';return true;" 

Books:
JavaScript: The Definitive Guide: Activate Your Web Pages O'Reilly by David Flanagan
JavaScript, A Beginner's Guide, Third Edition by John Pollock
jQuery Cookbook: Solutions & Examples for jQuery Developers, O'Reilly, by Cody Lindley
Top 10 Best JavaScript Books that Beginners should Read - tripwire magazine
5 JavaScript Books Worth Every Cent

Links:
JavaScript and HTML DOM Reference at w3schools.com
Easy to Style jQuery Drop Down Menu Tutorial | Queness
WebReference.com
  How to Use a JavaScript Query String Parser
  JavaScript and Ajax Tips & Tutorials

Acknowledgement:
Thanks to Evan Willams for advice and support. See New Holland Press Blog