Anatta basically means: "not self", "not me", or "not mine"; the impersonal nature of existence. We can see it in material things; things arise from the Four Great Elements. These Four Great Elements are put together into material things which we then label as "mine", but actually that is just the concept mind at work. Within that particular object that we label as "mine", there is the characteristic of Anatta, that is "not self", "not mine". Because it is made of the Four Great Elements, it is impermanent - it arises, changes, passes and returns to nature - so it cannot truly be mine in the real sense.
We can also see this in our thoughts - they arise and they pass due to causes and conditions. Feeling: the pleasant, unpleasant, and neutral feelings that arise coming from the sense doors – they arise and they pass due to causes and conditions. Sometimes we label them as "mine", but because they arise and they pass due to causes beyond our power to have total control, they cannot truly be mine. It's sometimes a difficult thing to accept that we don't have control over things and we can't claim them to be permanently mine; but, as we understand the impermanent nature of things and especially this Law of Cause and Effect, we let go of the wish to claim something to be forever mine.
Perhaps you can understand Anatta a little bit by the analogy of a river. The Mississippi River exists, right? It's right there on the map; but if you go to the side of the Mississippi River and you look at one spot in the middle of the river, is it the same water going by? We see it's constantly changing, but the concept, "Mississippi River", is always the same.
So we have to see beyond the surface appearance of things in order to see the impermanent nature of things - things flowing by due to cause and effect. Then we can come into more harmony with this impersonal nature of things -- Anatta, "not me", "not mine". It helps us to be less attached because we realize that we can't make things permanently mine. They're not ours in the beginning, and they will return to nature following the Law of Cause and Effect.