I suggest you first try to follow it yourself, maybe copy and play with A1 and see what happens, maybe copy aside parts of the formulas and see what they output.

Then you can read the writeup I wrote in response to another commenter (the guy who wrote the original Apps Script VM).

Brainfuck is a stack-based language with only 6-8? syntactic elements for manipulating the stack. + increments the current stack element, - decrements it. > increases the stack pointer and < decreases it. [ and ] have to with conditional jumping I believe. And it is common to convert the elements in the stack to ascii characters to display a result.

So if you go to the orange section of the sheet you see where the program state is displayed. Each row represents the state of the program at that point. The "Out" column is the stack represented as ASCII characters. The "Cursor" column is the stack pointer. The "IP" column is the instruction pointer (which instruction you're currently looking at). The "Instruction" column is the instruction being done at that point in time. The "Cells" column is the stack displayed from left to right.

I may be a little off but that is the general idea.