Very simply, it means that a person is free from greed, free from aversion, and free from ignorance of reality. So, if you still have some greed, if you still have some aversion, if you're still ignorant of reality, then you're not enlightened yet. It's a very simple definition.
Within the scriptures, it's interesting to see that when the Buddha taught about what is called Nibbana or the state of enlightenment (the Pali word is Nibbana, the Sanskrit word is Nirvana), he never said what it is. He said what it is not. He said it's a place where nothing is born, and nothing dies. Now for starters, we can't understand that. Everything we know has origination and dissolution, a birth and a death. We can't understand that there can be anything which is never born and never dies. He starts off with that. Immediately it's beyond our realm of actually knowing what it's like.
Now an example that I give to illustrate this is: go to some little village here in Thailand, really out in the outback, where they've never had many farangs (foreigners) ever come. Find a little kid, six or eight years old, and by and large they have never eaten cherries. Try to describe a cherry to them. Can they possibly understand what it is? You can tell them, well it's not a guava, when they start thinking it's like a guava. "Is it a banana?" they say; "No it's not a banana." "Is it a papaya?" "No, it's not papaya." You can tell them what it's not, but if you try to describe a cherry to them, it's really impossible for them to know what you're meaning using words. But if you give them a cherry, they'll see it very clearly, they'll eat it, they'll taste it, then they'll know what a cherry's like. So, as far as actually knowing what enlightenment is, you've really got to be enlightened, otherwise the words are just not quite enough.