That is a very good question, and ultimately depends on what the meaning of the word “is” is.
Arduino refers to a family of products, all based around the same concept: a microcontroller, on a small form factor circuit board, augmented with additional circuitry to make the platform simple to use and learn. The product used in projects on this blog is the Arduino Uno, so named because it was the first product they officially released. (Note: I bought my Uno in 2013, and the design has undergone a few incremental changes since then. However, the differences between the Uno used on this blog and one purchased brand-new today are only visual; all programs, wiring diagrams, breadboard layouts, etc. will be identical.)
Top view of Arduino Uno. Image source: arduino.cc
The Uno is based on the Atmel ATmega328P microprocessor. An in-depth technical description of this processor is beyond the scope of this website, but the Arduino platform takes this microprocessor and builds around it a platform that includes a USB port, a USB controller, a bootloader and multiple jumper sockets connected to the various input/output devices on the processor. This platform allows the Arduino to be used by starters to build circuits without needing any knowledge of fabrication techniques; you don’t need to solder together connections, which is precise and frustrating; etch your own PCBs, which requires harsh chemicals and can ruin components if not done properly; or flash program any devices, which requires expensive hardware and extensive knowledge of programming in Assembly. Devices can be connected by sticking jumper wires into a breadboard, and programs can be written in C and transferred via USB cable.
[[homebrew image of arduino]]
In addition to the simplicity and ease of use with which the Arduino has been designed, there is a massive community of homebrewers, with diverse spectra of backgrounds and experiences.