Specification is a set of rules that will govern language implementations. It is going to have evolutions, new versions are created with news of what the language should have and the implementations that wish to conform to the most current specification should implement.
ES6 is EcmaScript 6. EcmaScript is the official name of what we know as JavaScript, which is actually the name created by Mozilla. This version is also known by the year of its publication, in the case 2015.
JavaScript is an implementation of EcmaScript. You have more information about this in another question .
ECMA is an international regulator of European origin. Similar to ISO which is more world-wide. Just like we have ABNT in Brazil. In general, approving an Ecma regulation is easier than ISO so it is common to opt for it.
There is a website with all the news from ES6 . The official specification can be obtained from the official website .
You can follow the implementation of this version in browsers. For example in Mozilla . You can also view a comparative table .
We are already working with version 7 (2016) . Soon we will have ES.Next, which does not have a definitive name yet.