What is the library m in C++ linker? Following this guide, it says to include a library in the C++ Linker called m. What is this for?

Specifically, Your second Arduino project. 

4) Configure project

5th dot point:


  AVR C++ Linker -> Libraries: Under libraries, add arduino_core and m (in that order). Under path, add the path to the correct core library, e.g. "${workspace_loc:/arduino_core/328P_16MHz}"
The m library is the "math" library. You have to link with it in most flavours of gnu compilers (it is typically not required in other, as it is included in the standard lib) when using functions and stuff from the header file "math.h".