Nowadays a successful website or web application makes use of several technologies. The LAMP stack is one particular set of technologies commonly used to build web sites.
The other two parts of the LAMP stack involve setting up and managing the web server. It is often (but not always) considered set it and forget it type administrative work. In larger organizations this job is considered a separate role from the people who write code. Sometimes this position is called DevOps (short for Developer Operations) or simply System Administrators. It is normal to have one DevOps person supporting several developers. In other words, most businesses typically need development work (i.e. writing code) more consistently than they need server setup and server maintenance.
Because writing code is more common than server stuff, the average developer is good at writing code. A full stack developer however, will have the experience required to be able to work on any part of the infrastructure that supports the web site, regardless of whether it involves configuring a server or writing code.