Arduino is a single-board micro-controller. With a little bit of code, you can manipulate objects in the physical world. Typically, C++ and C languages are used to program the Arduino, but any language can be used. As the Arduino is not a computer and is simply a board, it is best for simple, repetitive tasks.
There are so many things you can do with the Arduino board. If you attach a motion sensor to an Arduino, you can create simple alarm systems, telling it to send you a message or flash bright lights when triggered. Add a gas sensor and you can create your own fire alarm. Do you have a physics lab you need to do? You can add many things to the Arduino to measure force, velocity, acceleration, etc.
For starting out, you can look at one of these 10 beginner projects:
https://create.arduino.cc/projecthub/RoyTobby/10-awesome-beginner-arduino-projects-78a6a6
An Arduino-powered thermostat:
http://www.makeuseof.com/tag/make-your-own-temperature-controller-with-an-arduino/
Have a look at a Bluetooth RC Car:
https://create.arduino.cc/projecthub/windowsiot/bluetooth-rc-car-with-remote-arduino-5f09c9
Does anybody like chess? https://create.arduino.cc/projecthub/Maxchess/wooden-chess-board-with-piece-recognition-872ffb