Arduino code is C++. The Arduino core functions are simply a set of C++ classes and libraries you can use. It is built and compiled using the GNU gcc/g++ compiler. Your setup() and loop() functions are simply placed into the mandatory main() function (right here actually--notice the file is "main.cpp", which is a C++ source file) automatically for you and there is some extra preprocessing done to make sure it is a valid C++ program (ex: scanning for all function prototypes [aka: declarations] for you so you can use a function even though its prototype comes later in your .ino file). Much of Arduino is written in a "C style", however, and therefore requires the # extern "C" {} braces around it to prevent C++ from "name-mangling" (also known as "name decorating/name decoration") function calls to C functions implemented by AVR-libc, which is the C implementation for the ATmega328 and other AVR-architecture microcontrollers.

"Can I program the Arduino board in C?
In fact, you already are; the Arduino language is merely a set of C/C++ functions that can be called from your code. Your sketch undergoes minor changes (e.g. automatic generation of function prototypes) and then is passed directly to a C/C++ compiler (avr-g++). All standard C and C++ constructs supported by avr-g++ should work in Arduino. For more details, see the page on the Arduino build process."

Source: https://www.arduino.cc/en/Main/FAQ#toc13

Update: Eclipse setup

See my answer here: What are the other IDEs for Arduino?. I wrote a detailed PDF to describe setup.

Arduino is C and C++ (it is a mix of the two, linked together); there is no "Arduino" programming language

Arduino code is C++. The Arduino core functions are simply a set of C++ classes and libraries you can use. It is built and compiled using the GNU gcc/g++ compiler. Your setup() and loop() functions are simply placed into the mandatory (meaning: required by both C and C++ in order to even be considered a valid program) main() function (right here actually--notice the file is main.cpp, which is a C++ source file) automatically for you and there is some extra preprocessing done to make sure it is a valid C++ program (ex: scanning for all function prototypes [aka: declarations] for you so you can use a function even though its prototype comes later in your .ino file). Much of Arduino is written in C, however, and therefore requires the # extern "C" {} braces around it to prevent C++ from "name-mangling" (also known as "name decorating/name decoration") function calls to C functions implemented by AVR-libc, which is the C implementation for the ATmega328 and other AVR-architecture microcontrollers.

"Can I program the Arduino board in C?
In fact, you already are; the Arduino language is merely a set of C/C++ functions that can be called from your code. Your sketch undergoes minor changes (e.g. automatic generation of function prototypes) and then is passed directly to a C/C++ compiler (avr-g++). All standard C and C++ constructs supported by avr-g++ should work in Arduino. For more details, see the page on the Arduino build process."

Source: https://support.arduino.cc/hc/en-us/articles/360018448219-Can-I-program-the-Arduino-board-in-C-

Update: Eclipse setup

See my answer here and my document here: Eclipse setup instructions on a new Linux (or other OS) computer. I wrote a detailed PDF to describe setup.

The Arduino language is C++ (albeit usually implemented in a style more like "C with classes," which is actually fairly common in the embedded systems microcontroller world). End of story. Enough with people thinking it's a different language already! It uses the g++ compiler.

Proof:

Enable verbose output during compilation in the Preferences and upload and you'll learn a lot just reading those lines.

Here's some additional insight:

My own words:

Arduino code is C++. The Arduino core functions are simply a set of C++ classes and libraries you can use. It is built and compiled using the GNU gcc/g++ compiler. Your setup() and loop() functions are simply placed into the mandatory main() function (right here actually--notice the file is "main.cpp", which is a C++ source file) automatically for you and there is some extra preprocessing done to make sure it is a valid C++ program (ex: scanning for all function prototypes [aka: declarations] for you so you can use a function even though its prototype comes later in your .ino file). Much of Arduino is written in a "C style", however, and therefore requires the # extern "C" {} braces around it to prevent C++ from "name-mangling" (also known as "name decorating/name decoration") function calls to C functions implemented by AVR-libc, which is the C implementation for the ATmega328 and other AVR-architecture microcontrollers.

Arduino's words:

"Can I program the Arduino board in C?
In fact, you already are; the Arduino language is merely a set of C/C++ functions that can be called from your code. Your sketch undergoes minor changes (e.g. automatic generation of function prototypes) and then is passed directly to a C/C++ compiler (avr-g++). All standard C and C++ constructs supported by avr-g++ should work in Arduino. For more details, see the page on the Arduino build process."

Source: https://www.arduino.cc/en/Main/FAQ#toc13

When to use the Arduino library vs pure C or C++?

So, use the Arduino language where it simplifies things, and write your own functions where you need more specialization. I do recommend getting away from the IDE quickly though for writing code--just use it for compilation. Set the IDE preferences to use "External Editor." Then use a professional source code editor/IDE such as Sublime Text 3, Atom, Visual Studio Code, or Eclipse CDT to write your code. You can then click back to the Arduino IDE to compile and upload. If you go with Eclipse, there are ways to do that in Eclipse (see the other answers here, and see the Arduino playground Eclipse article here too) so consider using those techniques too.

The Arduino language is C++ (albeit usually implemented in a style more like "C with classes," which is actually fairly common in the embedded systems microcontroller world). End of story. Enough with people thinking it's a different language already! It uses the g++ compiler.

Proof:

Enable verbose output during compilation in the Preferences and upload and you'll learn a lot just reading those lines.

Here's some additional insight:

My own words:

Arduino code is C++. The Arduino core functions are simply a set of C++ classes and libraries you can use. It is built and compiled using the GNU gcc/g++ compiler. Your setup() and loop() functions are simply placed into the mandatory main() function (right here actually--notice the file is "main.cpp", which is a C++ source file) automatically for you and there is some extra preprocessing done to make sure it is a valid C++ program (ex: scanning for all function prototypes [aka: declarations] for you so you can use a function even though its prototype comes later in your .ino file). Much of Arduino is written in a "C style", however, and therefore requires the # extern "C" {} braces around it to prevent C++ from "name-mangling" (also known as "name decorating/name decoration") function calls to C functions implemented by AVR-libc, which is the C implementation for the ATmega328 and other AVR-architecture microcontrollers.

Arduino's words:

"Can I program the Arduino board in C?
In fact, you already are; the Arduino language is merely a set of C/C++ functions that can be called from your code. Your sketch undergoes minor changes (e.g. automatic generation of function prototypes) and then is passed directly to a C/C++ compiler (avr-g++). All standard C and C++ constructs supported by avr-g++ should work in Arduino. For more details, see the page on the Arduino build process."

Source: https://www.arduino.cc/en/Main/FAQ#toc13

When to use the Arduino library vs pure C or C++?

So, use the Arduino language where it simplifies things, and write your own functions where you need more specialization. I do recommend getting away from the IDE quickly though for writing code--just use it for compilation. Set the IDE preferences to use "External Editor." Then use a professional source code editor/IDE such as Sublime Text 3, Atom, Visual Studio Code, or Eclipse CDT to write your code. You can then click back to the Arduino IDE to compile and upload. If you go with Eclipse, there are ways to do that in Eclipse (see the other answers here, and see the Arduino playground Eclipse article here too) so consider using those techniques too.

Update: Eclipse setup

See my answer here: What are the other IDEs for Arduino?. I wrote a detailed PDF to describe setup.