Even though we usually view our images at arm's length, so to speak, sometimes it's necessary (and tempting) to view them up close - reeeeeeeally close - to see the pixel detail.
How do I "pixel peep"?
By viewing at 100% in your imaging program. 100% means that one image pixel is being represented by one screen pixel. If you view smaller than that, you're not getting a true representation of the pixels. If you view larger than that, you're getting an exaggerated representation, and that can make things seem worse than they really are.
Oh, gee, that's huge!
Yes, it is. 100% size on screen is much bigger than 100% size in print. If we make the broad assumption that the average print resolution is 300ppi, and the average LCD screen resolution is 100ppi, then your on-screen view will be three times longer/wider than the corresponding print view.
(Out of interest, you can check the exact resolution of your screen by doing this).
Why would I want to pixel-peep?
I can think of three main reasons - noise, focus, and sharpening.
1. Noise
We pixel-peep to see how clean or noisy our image is. Noise is that speckled graininess. It's a result of a high ISO setting; or underexposure which has been corrected in post-processing; or most commonly a combination of both.
Nothing beats preventing noise in camera, of course. Better lighting and lower ISO are your best defence against noise. But inevitably you will always have some noise in your images, so make sure you never forget to remove it.
Recently I've seen claims that noise can be introduced when focus is missed. This is not true. Noise issues are noise issues, and focus issues are focus issues. They can exist together, or separately, but are not directly related. More like "cousins by marriage", as it were. The poor lighting that forced you to increase your ISO setting may also have caused you to miss your focus; but that's as close as the relationship gets.
It's perfectly possible to have a completely noise-free image, with poor focus. Conversely, it's perfectly possible to have a well-focused image with a lot of noise. The latter is problematic, because the noisy pixels can't render the fine detail properly, and therefore don't do justice to your great focus.
When you're running any kind of noise removal software, make sure you only view at 100% or higher, and be aware that any kind of noise removal is going to (at least partially) ruin fine detail in your image. That's the trade-off.
2. Focus
Focus is the holy grail, isn't it? We want our portraits to have eyelashes that could cut diamonds. Focus is the one thing that can make you sigh, shake your head sadly, and delete an otherwise wonderful photo.
There are only a few things that Photoshop can't fix, and focus is right at the top of that list. If you don't hit it in camera, the best you can hope for is to (a) print small and hope nobody notices; (b) apply some kind of sharpening to try to disguise the problem; or (c) run an artistic effect on the photo to pretend it never happened.
You can mess up your focus in two ways: by missing the focal plane (and ending up with the tip of somebody's nose in focus instead of their eyes, for example); or when your subject moves faster than your shutter does, resulting in motion blur.
The two types of focus error are easy to distinguish once you've seen them both a few times. Motion blur ends up with a slight (or not-so-slight) double image, whereas a missed focal plane just results in softness. Of course, both problems can exist simultaneously sometimes.
Motion blur is a shutter speed problem; focal plane blur is a focus problem, usually associated with aperture. Those blurred backgrounds from wide apertures are lovely, of course, but it sure does narrow your depth of field, and makes it much easier to miss the focal plane.
One more thing to mention about focus. Don't expect eyelashes to be as clear on a group shot as on a close-up portrait. There just aren't enough pixels to go around. On a close-up portrait, there can easily be 100 pixels per eyelash. On a person in a group shot, there might only be 100 pixels available to render the whole eye! Lots of photographers, when just starting out, lament their "missed focus" in a group shot; whereas their focus has been perfect. You just need to have different expectations, is all.
3. Sharpening
While noise and focus are all about the camera, sharpening is exclusively a post-production matter. Whenever you apply sharpening to your image, make sure you view at 100% to accurately preview the effect.
Sharpening for web is easy, because WYSIWYG. You are sharpening at the exact size that people will view the image on your site.
Sharpening for print is more difficult, because as I mentioned earlier, you are viewing your image about three times larger on the screen than it will be in print. So it takes a bit of practice to know what's the right strength of sharpening.