Slax core is a set of hardware drivers, programs and system libraries, which are needed by almost every other module. It is the most important part of Slax, which takes care about the system startup and shutdown. Furthermore, it provides a simple shell prompt to execute commands and start software.
This module is already included in official Slax release, so you don't need to download it separately. However, you may need to add it while using the 'build Slax' feature of this website.