Using __block and __weak

__block is a storage qualifier. It specifies that the variable should directly be captured by the block as opposed to copying it. This is useful in case you need to modify the original variable, as in the following example

__block NSString *aString = @"Hey!"; 
void(^aBlock)() = ^{ aString = @"Hello!" }; // without __block you couldn't modify aString
NSLog(@"%@", aString); // Hey!
aBlock();
NSLog(@"%@", aString); // Hello!

In ARC this causes the variable to be automatically retained, so that it can be safely referenced within the block implementation. In the previous example, then, aString is sent a retain message when captured in the block context.

Note that this isn't true in MRC (Manual Reference Counting), where the variable is referenced without being retained.

Marking it as __weak causes the variable not to be retained, so the block directly refers to it but without retaining it. This is potentially dangerous since in case the block lives longer than the variable, since it will be referring to garbage memory (and likely to crash).

Here's the relevant paragraph from the clang doc:

In the Objective-C and Objective-C++ languages, we allow the __weak specifier for __block variables of object type. [...] This qualifier causes these variables to be kept without retain messages being sent. This knowingly leads to dangling pointers if the Block (or a copy) outlives the lifetime of this object.

Finally the claim that __block can be used to avoid strong reference cycles (aka retain cycles) is plain wrong in an ARC context. Due to the fact that in ARC __block causes the variable to be strongly referenced, it's actually more likely to cause them.

For instance in MRC this code breaks a retain cycle

__block typeof(self) blockSelf = self; //this would retain self in ARC!
[self methodThatTakesABlock:^ {
    [blockSelf doSomething];
}];

whereas to achieve the same result in ARC, you normally do

__weak typeof(self) weakSelf = self;
[self methodThatTakesABlock:^ {
    [weakSelf doSomething];
}];

You should use __block if you want to change variable value in block.

e.g:

__block BOOL result = NO;
dispatch_sync(dispatch_get_main_queue(), ^{
  ...
  result = YES;
  ...
});

You should use __weak if you want to avoid retain cycles.

e.g.:

__weak typeof(self) wself = self;
self.foobarCompletion = ^{
  ...
  wself.foo = YES;
  ...
};

You can combine them if there is a need.