If you are programming with JavaScript, knowing about ES3, ES5 & Harmony specifications and their usage will be useful. Here's a plain & simple explanation of them for your easy understanding.
ECMAScript
If we look into the history of JavaScript, it was originated from a side project of Brendan Eich called "Mocha". In 1995, it was shipped with Netscape browser as "LiveScript" and it soon renamed as "JavaScript" (mainly from the influence of Sun Microsystems). Due to the quick popularity of JavaScript, Microsoft also decided to ship it with Internet Explorer in 1996. Microsoft's implementation had slight differences from the original, thus they aptly named it as "JScript".
As browser wars between Netscape and Microsoft fired up, Netscape soon pushed JavaScript to Ecma International for standardization. Ecma accepted the proposal and began the standardization under the ECMA-262 standard. As a compromise for all organizations involved in the standardization process, ECMA-262 baptized this scripting language as "ECMAScript".
Even though we still call it as JavaScript, the technically correct name is ECMAScript.
ES3
Over the years, Ecma has released different editions of ECMAScript standard. For the ease of use we call these standards as "ESx", where x refers to the edition. So the 3rd edition of ECMAScript is known as ES3. ES3 can be considered as the most widely adopted edition of ECMASCript.
The most outdated browser in mainstream (aka Disease) Internet Explorer 6 is compliant with ES3. Sadly, other common IE versions(7 & 8) are also only compatible with ES3. Early versions of most other browsers also supported ES3. This means all JavaScript features you commonly use are part of ES3. Most JavaScript libraries, frameworks, tutorials, best practices and books written in the past are based on these features standardized in ES3.
Source-to-source compilers such as CoffeeScript, which aims to run everywhere, compiles its code to be compatible with ES3.
If you are interested in reading the full ECMAScript 3rd edition specification, you can download it from here.
ES5
After years of split and conflict of interests ECMA's Technical Committee came to an agreement in 2008 to follow two paths for the future development of ECMAScript. One as an immediate plan to overcome the issues ES3 specification (then called as ES3.1). Another with a long term vision to evolve the language for the modern requirements. They also decided to kill ES4 specification, which was under development to support the above plans.
The ES3.1 edition was finally released as ES5 in 2009. Some of the notable features in this edition were Native JSON support, better Object creation and controlling options, utility Array functions and the introduction of strict mode to discourage the usage of unsafe and poorly implemented language features. You can read a detailed introduction about ES5 features in Opera blog.
Full support for ES5 in major browsers were introduced from the following versions - Firefox 4, Chrome 7, Internet Explorer 9 and Opera 11.60. Safari 5.1 (and mobile Safari) in iOS5 do support all of ES5 features except for Function.bind. Also, IE9 doesn't support the strict mode option. Juriy Zaytsev provides a comprehensive compatibility table of ES5 features, which I recommend you to bookmark.
So is it safe to use ES5 features in our JavaScript code? Answer to that largely depends on your user base. If majority of your users comes from Internet Explorer 6, 7 & 8, code with ES5 features will break for them. One way to solve this problem is to use ES5 shims for unsupported browsers. You may decide which shims to include depending on the features you use in your code. Also, if your code is already depending on a utility library such as Underscore.js, which also provides similar features to ES5 you may continue to use it. Most utility libraries will use the native implementation if available, before falling back to its own implementation.
If you are writing server-side JavaScript based on Node.js you can freely use ES5 features. Node.js is based on the V8 JavaScript engine, which is fully compatible with ES5. Another thing to consider is whether you should write your server-side JavaScript using CoffeeScript. If you are doing so, you are limiting your ability to use native ES5 features. As I mentioned earlier CoffeeScript compiles only to ES3 compatible JavaScript and has custom implementations for ES5 features such as bind. However, this is still an open issue with discussions, suggesting CoffeeScript may add the option to compile ES5 compatible code in future.
For the full reference of ES5, I recommend using the annotated HTML version done by Michael Smith - es5.github.com
ES.Next (Harmony)
The long-term plan for the ECMAScript in 2008 meeting, was code-named Harmony. Committee is still accepting proposals for this edition. Most probably, this will become the ES6, but given the past track-record of ECMA-262 ES.Next would be more suitable name until a release is made.
Currently planned features for Harmony sounds promising. Brendan Eich has shared some ideas for Harmony which seems to make the language more concise and poweful. Also, his presentation on Proxy Objects in Harmony sounds awesome.
SpiderMonkey and V8 JavaScript engines has already started implementing some of the Harmony related features, such as Proxies and WeakMaps. It would be still premature to use these features at the client-side (in Chromium browser you need to explicitly enable Harmony features via a special flag). Node.js 0.7, will ship with v8 version 3.8 giving you the opportunity to tase some of the Harmony features in server-side.