Minecraft is a game where you dig (mine) and build (craft) different kinds of 3D blocks within a large world of varying terrains and habitats to explore.
In this world the sun rises and sets as you go about your work, gathering materials and making tools. There is rain and the occasional lightning storm, and animals that you can tame, farm or use for food. Depending on which mode you’re playing in, you might also need to fight for your survival against hunger, danger and monsters that come out at night.
A question often asked is, what is the objective? The answer is quite simple, there is no objective. There are achievements that you will be awarded for various accomplishments, some as small as crafting your first pickaxe, and some as monumental as defeating the Ender Dragon. However, there is no point at which you can declare that you have “finished” the game. You can keep building structures, exploring new lands and taming rare animals for as long as you like. You are only limited by your imagination and your sense of adventure.
An excellent step-by-step guide for Minecraft beginners, is Paul Soares Jr’s How to Survive and Thrive in Minecraft.