Your brain filters out your nose in a few ways: One, your nose blocks part of the visual field of both your eyes, so when your brain receives the information your eyes are transmitting, it constructs a whole image from the unblocked information from both
eyes. Two, your nose is in your peripheral vision, so you don't notice it as much. Three, it's so close to your eyes that it's out of focus, because you're focusing on things that are farther away.
As it turns out, your brain filters out a lot of visual information, not just your nose. If it didn't, you would be overwhelmed with so much sensory input that you wouldn't be able to function. This is, for example, why people who wear
glasses don't usually notice them.
Now, that doesn't mean you can never see your nose. In fact, you can see it right now. Close one eye, then the other. You'll be able to see your nose on the side of your eye. But when you open your eyes again, it disappears.
This illustrates the importance of getting regular
eye exams, especially if you're at risk for developing
glaucoma.