I don't claim to be an expert on learning intentions and success criteria, I'm merely sharing what I think about their importance, particularly with relation to my domain in computing science.
From being a teacher for a year now, I have come to realise that a lot of teachers when I was at school would simply assume that the class knew what they were learning when the teacher started off the lesson with something along the lines of "right guys, today we're going to be learning about x and y". However, this is not as clear as it can be through the use of concrete learning intentions.
As a computing science teacher (an NQT, but still a teacher), I often find that saying 'we're going to look at variables' is just not enough to give pupils an understanding of what they are learning, the significance of it in relation to existing learning and teaching and where the boundaries of the lesson are.
Taking the above example with regards to variables and the PHP language, one might assume we are talking about local variables such as $x = 10, but we don't want to talk about the superglobals variables in PHP, simply the local variables. Some pupils might come across these and attempt to find out more about them too. Without clear learning intentions, they'd be absolutely in the right doing this.
So why are learning intentions so important in these situations? I often like to think of them as frameworks that determine the boundaries and that remain in place through the lesson or lessons. Often with a simple introduction about what we are going to be learning, there is not enough depth to explain what we are going to learn and what we are not going to learn. Learning intentions are also really good because they can remain there for the whole lesson to prevent deviation from the actual learning, and whilst it is great that pupils learn more, I often feel that without clear intentions that pupils can strive into the rough and cannot get back out again. Further to this, whilst it's great for those who have excelled in the lesson to go on and learn more, it should clearly be signposted by the teacher that it is okay to do this, otherwise the pupil may end up attempting something way beyond their level.
Further to this, it helps you as a teacher making sure that you do not cover too much. If your own lessons are structured around the learning intentions and what you want the pupils to learn in that lesson you can clearly lay out the lesson around them. By doing this you can also see whether or not you are trying to do too much in one lesson.
So my main love for learning intentions comes from the fact that they keep pupils on track, which is particularly important in computing as it prevents pupils from getting lost at sea and it also helps you as a teacher to ensure you don't go too far with the lesson.