C and C++ are the most common and "natural" programming languages in the Linux environment. There are literally millions of programs written in C and C++! From the compiler's point of view, most of them can be compiled for and executed on the LTPP3 board.
If you are used to working with Linux on the PC, you must consider some differences between the desktop Linux and embedded Linux running on the LTPP board:
To build a program for the LTPP3 board you will need a cross-compiler (a compiler capable of creating an executable code for a platform other than the one on which the compiler is running), some build-helpers (like Make or Cmake, etc.), as well as correct header files and precompiled libraries. All this, combined into a single installation package is often referred to as the SDK (Software Development Kit) platform.
Tibbo maintains its own LTPS (LTPP) SDK published in the LTPS downloads area. It contains everything you may need to build a binary for the LTPP board.