Say you want to perform in action (in this case, logging "Foo"), while doing something else (logging "Bar"). Normally, if you don't use concurrency, one of these actions is going to be fully executed, and the other run will run only after it's completely finished. But with concurrency, you can make both actions run at the same time:

dispatch_async(dispatch_queue_create("Foo", DISPATCH_QUEUE_CONCURRENT), ^{
    for (int i = 0; i < 100; i++) {
        NSLog(@"Foo");
        usleep(100000);
    }
});

for (int i = 0; i < 100; i++) {
    NSLog(@"Bar");
    usleep(50000);
}

This will log "Foo" 100 times, pausing for 100ms each time it logs, but it will do all this on a separate thread. While Foo is being logged, "Bar" will also be logged in 50ms intervals, at the same time. You should ideally see an output with "Foo"s and "Bars" mixed together

When performing tasks asynchronously there typically becomes a need to ensure a piece of code is run on the main thread. For example you may want to hit a REST API asynchronously, but put the result in a UILabel on the screen. Before updating the UILabel you must ensure that your code is run on the main thread:

dispatch_async(dispatch_get_global_queue(DISPATCH_QUEUE_PRIORITY_DEFAULT, 0), ^{
    //Perform expensive tasks
    //...

    //Now before updating the UI, ensure we are back on the main thread
    dispatch_async(dispatch_get_main_queue(), ^{
        label.text = //....
    });
}

Whenever you update views on the screen, always ensure you are doing so on the main thread, otherwise undefined behavior could occur.

dispatch_group_t preapreWaitingGroup = dispatch_group_create();

dispatch_group_enter(preapreWaitingGroup);
[self doAsynchronousTaskWithComplete:^(id someResults, NSError *error) { 
    // Notify that this task has been completed.
    dispatch_group_leave(preapreWaitingGroup);  
}]

dispatch_group_enter(preapreWaitingGroup);
[self doOtherAsynchronousTaskWithComplete:^(id someResults, NSError *error) { 
    dispatch_group_leave(preapreWaitingGroup);  
}]

dispatch_group_notify(preapreWaitingGroup, dispatch_get_main_queue(), ^{
    // This block will be executed once all above threads completed and call dispatch_group_leave
    NSLog(@"Prepare completed. I'm readyyyy");
});

Update 1. Swift 3 version.

let prepareGroup = DispatchGroup()
prepareGroup.enter()
doAsynchronousTaskWithComplete() { (someResults, error) in
    // Notify that this task has been completed.
    prepareGroup.leave()
}

prepareGroup.enter()
doOtherAsynchronousTaskWithComplete() { (someResults, error) in
    // Notify that this task has been completed.
    prepareGroup.leave()
}

prepareGroup.notify(queue: DispatchQueue.main) {
    // This block will be executed once all above threads completed and call dispatch_group_leave
    print("Prepare completed. I'm readyyyy")
}