The basic idea is that there is a world "out there", and then each person has a mental model of that world. Our actions are not based on the external world, but on our internal model of it.
When sensory information comes in, we use that to update the model. The loop is something like:
1. Stimulus comes in.
2. Figure out what that means.
3. Use that to update the model.
4. Take action based on that.
5. See how our action affected the world and goto 1.
Step 2 is the tricky one. Stimulus is often ambiguous and our perceptions of it are imperfect. You see a flash of light. It could mean someone took a photo, the sun glinted off a moving object, or maybe just a spurious firing on our optical nerve. How do we know how to update the model based on that stimulus?
We can't just always assume the stimulus is fully accurate and blanket update the model based on it because there's a lot of noise in the data. We also can't just assume that whenever the stimulus disagrees with the model that it's noise and discard it. The whole point of perception is to update our model to reflect a changing world.
So we have to decide what a piece of stimulus means (since it's ambiguous) and how much confidence we have in that interpretation (since it's noisy). How might we decide a confidence level? All we know is our own model and that the external stimulus.
There are a bunch of different ways that involve things like estimating how likely a stimulus like that is to occur, our previous experience with misinterpreted signals (i.e. what we have learned about our own perceptual hardware), etc.
Of course, none of this is happening consciously. It's how the brain itself thinks.
The thesis of the article is that those with autism have this process miscalibrated where they treat external stimulus as much more precise (i.e. less noisy or ambiguous) than it actually is. The symptoms of autism are then emergent phenomena of how a brain might try to cope with that problem.