The "Anthropic Principle" is a philosophical concept that was posited by an astronomer and physicist named Robert Dicke, who noted that our observations about the universe must be limited to a specific collection of properties because we exist.
In other words: that we are around to observe the universe implies the universe must have properties that allow for the existence of life capable of doing such observation.
Thus, the universe must be a certain age, must contain certain elements, and so on, because if it didn't contain the things we require to exist, we wouldn't be here to notice that dearth.
There are two primary versions of this theory stemming from the main concept: the weak anthropic principle (WAP) and the strong anthropic principle (SAP).
The SAP makes the teleological claim that the universe has been fine-tuned or cultivated in some way to ensure that life arises and persists—more of an ideological statement than a scientific one—while the WAP says that the properties we observe in the universe that we could interpret as being too coincidental, and thus possibly the work of some kind of godlike watchmaker figure, are the only possible way things could have been, because had these variables not been as they are we wouldn't exist to speculate about them.
We couldn't very well look out into the universe and see that carbon hasn't formed for instance, because we are carbon-based life, and thus we couldn't have arisen during earlier periods of universal development when carbon didn't exist.
This is less a testable theory, then, and more a framing of how things seem to be based on the undeniable reality (in the context of this philosophical standpoint, at least) that we exist and are capable of observing the universe.
So while it's possible to look at physical reality and assume that it is as it is because someone or something wanted us to come into being, the WAP conception posits that there's no other way things could have been because if they were not as they are—at least in terms of variables that allow or disallow the emergence of human life (the mass of the electron, the strength of gravity, etc)—we wouldn't be having this conversation.
Coincidences that might be presented as evidence for higher beings that want us to exist, then, may be not coincidences, but rather necessary ingredients for us to be around to speculate on such things.
This doesn't mean that a universe without carbon cannot have life, as well, or that the other variables necessary for humans to have arisen are vital to the existence of something capable of observing the universe.
For those other theoretical sorts of life, though, their necessities would be (somewhat or dramatically) different from ours, which means their universal setup might never overlap with our own—which in turn would mean that their version of the Anthropic Principle would be conceptually the same, but the specifics would vary.
My take on WAP is that, if there are a gamut of universes out there and their number is large enough, the probability of existing an universe just like ours will approach 1 (one).