Specification is a set of rules that will regulate language implementations. It will have evolutions, new versions are created with novelties of what the language should have and the implementations that want to conform to the most current specification should implement.
ES6 is Ecmascript 6. Ecmacript 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 case 2015.
Javascript is an implementation of Ecmascript. Tem more information on this in another question.
ECMA is an international regulatory entity of European origin. Similar to ISO which is more global. Just as we have ABNT in Brazil. Generally, adopting an ECMA regulation is easier than ISO, so it is common to opt for it, and it may be a way to achieve ISO afterwards. And in some places in Europe requires this regulation for adoption in many circumstances, in other places not.
There is a site with all the ES6 news. To official specification can be obtained on the official website.
You can track how this version is implemented in browsers. For example in Mozilla. You can also see a comparative table.
We are already working with the version 7 (2016). Soon we will have ES.Next, which does not yet have a definitive name. Well, this was lagged, each year has a new ES.Next.
Linked: Coffeescript, Typescript and Javascript
– Jéf Bueno