I do not disagree with dmax999 except for one thing hitting is not peng. Peng is ward off and it is generally used to create distance between you and you opponent, Fingers and palm are relaxed with power in the wrists and forearm and the energy for peng comes from the back leg which is not hitting therefore it is not false peng it is not peng at all.
But back to the question at hand what is intention, it can be complicated... kinda... from a traditional Taiji point of view, but that complications has a lot to do with the translations and understanding of the terms shen, yi, shi and qi. Particularly shen, it translates as spirit which can have a completely different meaning to a Westerner than it does to a Chinese native.
You need Sandao which means you have to unify your shen (spirit), yi (thought/intension) and shi (posture). You control your Qi with your yi (thought/intension) and you use your qi to make your arm move for the punch or strike not your muscles. From the Taijiquan perspective it has more to do with bones and tendons than muscles.
From the Western perspective it is pretty much what dmax999 said, relax instead of tense for a hit or strike. Tensing of the muscles blocks the qi and therefore decreases power. And you get into the whole antagonistic muscles issue.
In Taiji you do the form slowly with intent in other words stay relaxed while doing the form but do the form as if there was actually an opponent there. Also it is important to have the proper posture. If I am not rooted or my center is, well, off center than my intension may exist but I have no root and no power and this is not good. If I have proper posture and am rooted and I do not use intension in my forms it a best becomes a dance. Shen as I can best understand it as it applies to Taiji is being present while doing the form. Many (not all) Taiji forms are done slowly so it is not difficult for the mind to wander off and start thinking about other things. If this is what you are doing your shen is not there and therefore you have no yi and it really doesn’t matter if you have posture or not because again you are doing what is at best a dance actually more like a zombie type dance. Your going through the motions but that is all.