One of the examples to demonstrate the idea of embodied or extended cognition is catching a fly ball: imagine you are in the outfield of a baseball game, and a ball gets hit in your general direction. How do you catch it?
The sense-plan-act model says: figure out the speed and direction of the ball ('sense'), calculate based on the laws of mechanics where the ball is going to land, and also use mechanics to figure out how you would get to that location ('plan'), and finally execute that very plan ('act').
Notice that on this view, perception and action are 'relegated' to 'mere' input and output: yes, of course you need a perceptual-motor system to be a cognitive agent in the world, but in the end that is really 'peripheral' to the stage where 'you figure it all out'.
Extended cognition is mostly a reaction to this sense-plan-act model; it states that perception and action are integral to one's mental processes. Indeed, rather than 'peripheral', perception and action are part and parcel of one's cognitive processes.
In the case of catching a fly ball: keep your eyes on the ball: if in your field of vision it moves to the left, then move to the left yourself. How far? For how long? Extended cognition says: for as long as the ball no longer moves to the left in your visual field ... and if it starts going to the right, well, then you move to the right as well. Likewise, if the ball in your visual field accelerates up, then it's going to land behind you, so you should back up.... and if it decelerates, then move forward. And just jeep doing this! In other words, no internal models of the world, and no complex calculations: just constant perception-action cycles.
Of course, both models have a perception-processing-action loop, but under extended cognition this loop is to be regarded as much tighter than under sense-plan-act. Indeed, whereas under sense-plan-act all the mental 'cognition' (the planning, the reasoning, the decision-making) is effectively claimed to be all 'in the head' (i.e. during the 'plan' phase) under the view of extended cognition, any explanation of one's mental and cognitive abilities will involve many perceptual-motor loops and, as such, 'cognition' is seen to be embedded in one's body, and extended into the environment.
Indeed, the explanation of how one catches a baseball is really quite different under these two models, and accordingly how the brain is involved in all this. Indeed, as such, the models become testable and falsifiable.... although we'll probably need some more advancements in neuroscience to see which model has the upper hand.