How to underwstand brainfuck

How to understand brainfuck?

It's easy, imagine a list, this lists has all it's values (contents) default to 0.
The length of the array (the list) depends on the system where brainfuck is run, in some systems it's a loop, in others the array can extend undefinetively
Now there are commands you use to change those values and move the pointer.
The pointer is the index of the array you're currently using.
There are 4 basic operators that are easy to learn

+ : Adds +1 on the index the pointer indicates
- : Decreases -1 on the index the pointer indicates
> : Moves the pointer right
< : Moves the pointer left

We can imagine the array with something like this: [0,0,0,0,0,0,0.....]
The pointer usually starts at the first index: [0,0,0,0,0,0,0.....]
                                                ^
The pointer is being represented with the '^' character below the array.
Some examples: I'm going to show visually what happens when you enter the operators
Operation:+
[0,0,0,0,0,0,0.....]  -> [1,0,0,0,0,0,0.....]
 ^                        ^
Operation:++++-
[1,0,0,0,0,0,0.....]  -> [4,0,0,0,0,0,0.....]
 ^                        ^
Operation:---- (Assume another array is being used)
[11,0,4,10,20,0,0.....]  -> [7,0,4,10,20,0,0.....]
 ^                           ^
Operation:> 
[7,0,4,10,20,0,0.....]  -> [7,0,4,10,20,0,0.....]
 ^                            ^
Operation:>>>
[0,0,0,0,0,0,0.....]  -> [0,0,0,0,0,0,0.....]
 ^                            ^
Operation:<<<
[0,0,0,0,0,0,0.....]  -> [0,0,0,0,0,0,0.....]
         ^                  ^
Operation:>>< (Yes, it's dumb, but explains the point)
[0,0,0,0,0,0,0.....]  -> [0,0,0,0,0,0,0.....]
 ^                          ^
Operation:++>+++>>>++
[0,0,0,0,0,0,0.....]  -> [0,0,2,3,0,0,2.....]
     ^                                ^
Operation:>>>+<++<
[0,0,0,0,0,0,0.....]  -> [0,0,2,1,0,0,0.....]
 ^                          ^ 
I believe those were enough examples, so we can begin talking about the "[" & "]" operators.
Basically they will do a loop which will repeat the same operators until when at the end of the loop the pointer is located in a zero value..
For example
Say we want too loop adding 4 (++++) at the next pointer twice
so:                                 
++ adds 2 to the current pointer: {2,0,0}
[ begins the loop
> moves the pointer to the right
++++ adds 4  {2,4,0}
< moves pointer back to the left (the beginning)
- decreases current value by 1 {1,4,0}
] ends loop, checks if current value is 0, if it's 0 stop, if it is not 0, it runs again
after a second run the array will look like this {0,8,0}
So the operation would be:++[>++++<-]
[0,0,0,0,0,0,0.....]  -> [0,8,0,0,0,0,0.....]
 ^                        ^ 
There's also the . and , operators which will scan and print the current bytes.  
and that's pretty much it, now you can enjoy the pleasures of brainfuck.