Imagine that the universe is a pond. That pond developed over the entire course of history, however long history actually is. Every atom, every molecule, every little bit of matter that makes up that pond is the result of the combination and destruction of every atom and every molecule that preceded it in the entire course of history, however long history actually is. Furthermore, that pond is determined by the results of every atom and every molecule that bounced off, dented, and chipped another molecule or atom over the course of history. Humanity is a speck of sand that is dropped into that pond. Humanity developed, like that pond, over the course of interactions throughout history. However long history is. When that speck of sand interacts with the rest of the pond, both are changed by the interaction. Therefore, there is no way to view the universe, as a person, without taking into account that the universe is exactly the way that it is because we are here and would be different if we were not. We are not responsible for this form, it just is because it is and we cannot view it without taking into account us.
Scientists deal with this on a less speculative form in any sort of field study, be it with other human cultures or various species of animals. It is impossible to observe without someway altering the habitat that you are observing, because you're very presence has already altered that habitat. The only thing scientists can do is minimize the amount that they are altering the environment as much as they can, whether by camouflage or distance, to preserve the data collected in the inquiry.
To go more esoteric and philosophical, it's like Ethan Hawke's character in Before Sunrise observes (paraphrased): There's nowhere I can go that I won't be, nothing I can say that I haven't said, nothing that I can look at that I can't see ... the only constant in every situation that I've ever been in is me.
The universe, the planet, the restaurant at the end of the universe ... none of this stuff needs humans to exist. But it is impossible for them to exist exactly as they exist without our involvement, whether we like it or not.
All this being said, I agree that the anthropic principle does sound a little bit like self-aggrandizing. To accept that all of those tiny tiny building blocks bounce around for all of those eons until humans were created and then all of our chromosomes bounced around for all of that time until they matched up exactly they way they matched up to form each of us on a planet that also has so many other examples of chromosomes matching up differently to form every type of animal, etc is pretty far fetched ... it's extremely unlikely, but it happened. To decide that must mean that we can reverse engineer our creation to figure out how everything was created, just because we know that some things had to occur because we're here ... well, that's just silly. It would be hard enough in a small environment to backtrack through all the possible combinations of data and make assumptions on the sliver of information that we might glean. It's pretty stupid to believe that we can do it based on what knowledge that we are able to perceive and collect from the larger universe. It's all speculation. Speculation based on some information, but still speculation.
Can I explain what happens in War and Peace because I know that it contains the word "the"? No, and further more, if I try I am operating under the assumption that the word "the" exists and that it exists in that book and ignoring the fact that the word "the" might itself be a translated form of a word that carries the same basic meaning in another language. I don't know Russian, but I know that they use a different alphabet than ours and that the word "the" contains other connotations (such as gender terms) in some foreign languages that we don't attribute to it in English, some or all might apply to a Russian form of the word "the". If we don't speak Russian and never seen Russian, then this is a lot to expect and is impossible to prove.
So, in it's most basic sense: anthropic principle means that the universe and everything else can only exist in the way that it exists right now because everything is as it is right now (including our presence). We cannot see a universe that we have not impacted because we are impacting it just by existing and taking up space in it. However, claiming that because we know that we exist, we can use the information of our existence to explain even a small part of everything, well, that's just silly talk.
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