Have you ever peeled an onion? If you look inside after peeling all the layers, you will find there is nothing in the center. The layers of the onion are some what similar to "our world" (sensory world) around us. This is similar to how we construct everything around us, layer by layer. We believe the body, feeling, perception, mental formations, and consciousness (the five aggregates), belongs to us and there is an 'I' in the middle of all of this. Just as the onion has no center, practice of The Noble Eightfold Path will lead us to the realization that there is no real "I' in the middle (non-self).
At a superficial level when we first study Dhamma to accumulate knowledge, we may understand this as a concept (Anatta-lakkhana Sutta). At a deeper level, with the practice of mindfulness meditation, it will enable us to realize this within us as our own wisdom. This realization is beyond comprehension and has to be experienced by oneself. This leads us to "let go" with ease, and to the final liberation from clinging to these aggregates, which are essentially the end of suffering (Dukka).
"Stop worrying about your body so much...you are just renting it anyway" (Post on Anatta or Non-self)