This term is frequently used, but I've not seen it defined here on the wiki.
When I (lv) talk about a core tcl command, I mean a command that is available after one builds one of the source distribution variations of tcl maintained by the TCT.
A core command of incr tcl would be one of the commands from the source distribution variations of that software as maintained by its project maintainers.
So if someone comes along and patches tcl for a new command, that new command - the new dict dictionary command for example - would be a core command because it is in the tcl 8.5 alpha source distribution.
Another use of the term core is for the memory image that can be produced if a program crashes and dumps core. A core dump can be a valuable help for debugging the crash, if you are an expert in understanding C stack traces and particularly if you configured tcl and the extensions with -enable-symbols .
DKF: A core dump is like the corpse of a process on Unix. Sometimes, you just have to carry out an autopsy to satisfy the coroner...
[Also Tcl Core Team, largely conducted through the tcl-core mailing list.]