Here's the short version. Brainfuck is an esoteric programming language. Urban Müller published it in 1993, with a compiler small enough to be a dare. He named it to shock. We will say the name, then we will write. The joke is the size of the alphabet, not the insult.
Lessons · Brainfuck · Lesson 1 of 10 · On the house
Eight glyphs and a tape
What Brainfuck is, and why anyone sat down to write it.

There are eight commands. That is the whole language. A greater-than. A less-than. A plus. A minus. A dot. A comma. An opening bracket. A closing bracket. Any other character is ignored — a comment, a note in the margin, a letter to yourself.
The alphabet
+-<>.,[]The machine underneath is simple on purpose. A long row of cells — a tape. A pointer that sits on one cell at a time. You change that cell, or you move the pointer, or you look at a cell and decide whether to loop. That is a program.
Quiz
How many commands does Brainfuck actually have?
Check
Type the eight glyphs in this order: plus, minus, greater-than, less-than, dot, comma, open bracket, close bracket. No spaces.
That's the door. Next time we sit with the tape itself, and we do not wave our hands at it.