This particular bit of doggerel has many different contexts, since it's so general. Often, like "obvious," it's a sign that a person hasn't thought things through. This one is also closely related to "I know what I saw!"
Intelligent Design: Many people claim that it's impossible not to see design everywhere. This strikes me as strange, since it seems "obvious" to me that the world wasn't designed, especially now that I know a thing or two about evolution. Some things work, and some things don't. The things that don't work die (natural selection) or get destroyed. (For instance, in the case of planets: If they aren't in an appropriate orbit, they fall into the sun or get flung out into the Kuiper Belt or wherever.) The world we see today is the result of a lot of self-pruning.
Psychic powers, Astrology, Tarot, etcetera: The perception of accuracy in these things stems mostly from the observer's mind, usually in the form of confirmation bias and the Forer effect: They're blinding themselves to mistakes and failures. For any of the believers reading this: This is one really good reason to make a recording of a reading. Your mind plays enough tricks with you, the psychic often doesn't need to.
Quackery: The appearance of improvement is not reliable when it comes to anecdotes. Human beings do not possess an infallible sense of status, or an infallible ability to determine the well-being of others. That's one reason the placebo effect exists: Anyone's perception can fail, especially in the direction of hope. You can see or feel what you hope or expect to. That's why things like double-blind placebo-controlled studies exist: Compare doing something to the illusion of doing something. If there's a big enough difference, it means you're really doing something. It's that simple.
Pareidolia "miracles": Try cloud-watching (or nebula-watching, see below) with a friend. You'll probably see a few things he can't, and vice-versa.
Data and Guinan are sitting at the row of windows, observing the spectacular view of the nebula.---
GUINAN: I see... a Samarian coral fish... with its fins unfolded...
DATA: I believe what you are seeing is the effect of the fluid dynamic processes inherent to large scale motion of highly rarified gas.
GUINAN: No... first it was a fish... now I see a Mintonian sailing ship...
GUINAN: (points) Right there -- see how the two swirls come up to form a mast...
DATA: I do not see it... It is interesting that people try to find meaningful patterns in things that are essentially random. I have noticed that the images they perceive can sometimes suggest what they are thinking about at that particular moment... Besides, it is clear that this cloud formation most closely resembles a "bunny rabbit."