Full stack is rather a cruel definition. I am sure must be floated by some smart manager,to differently motivate those who work hard. The definition of Full stack is also varying. I am sure that is also intentional, because then only Manager can get the work done from me by saying "common you  are a full stack developer!!!".

In that sense Full stake developer is one who can stretch beyond his core knowledge  to get the work done.

A product has many components which are developed using various skills.  However  most of the  use cases flows from one end to  other end. In this end to end movement, it  come across many hurdles and issues. If all the developers who knows only their domain then, it will result into a blame game, resulting into  a disaster.

Here comes the need of someone who just come in and  fix the issues. he know all the component and technology. It may be Javascript, PHP, linux, server he can work on any computer like linux windows, Even he can work on something that he don't know.

Full stack developer is neither a  leader nor a manager. because both need  a different skill  mostly  involving interaction with  people. Full stack develop is computer warm.  He knows everything  but he is  list recognized. and he is happy  in fact. he is the real software engineer. The other are here to earn money. but full stack developer is here because he just love doing it.

Generally startups and companies with limited resources are always in hunt of such hero. But chances of finding such people are very weak. 

 If I am to make a definition then, Full stack developer is the one guy who know front end, backend and the interfaces between each component and  the system which host the this solution and expert in GIT/SVN. for example in case of a Web solution, he knows the HTML,CSS,Javascript, and PHP,MYSQL, and also know the Apache/nginx configuration and how to host the site on a linux  server.

People says that the full stack developer also know the management skill. However I think it is really hight of cruelty. but Just considering the concern. I can say that he should at list be able to communicate his finding or  investigation to the management in a way that they understand. He many not be good in english but at list understand that people who he is communication are not Developers and they need to understand the severity of the issue at list the same level at which he is understanding.  The neither are leaders and Manager who will take care of convincing the client.  He should may not be good at estimation but roughly good enough to  give his opinion on estimation. He co operates manager in filling his spreadsheets, he must be friendly enough with manager and leader, at list he don't fight with them.
 
There are two well known example of full stack. they are LAMP and MEAN,  both are totally different  paths .  LAMP is for Linux+Apache+MySQL+PHP whereas MEAN is for Mongo+Express+Angular+Nginx.

I am being a full stack developer understand the pain of full stack developer very well.