Overprint preview is a PDF display technique that shows how a PDF file would be printed on a device that supports overprint (even though overprint is the effect of overprinting different inks). While overprint preview is a valuable technique that allows WYSIWYG (what you see (on screen) is what you get (in print)) for PDF documents, it is not supported by all or even most PDF viewers, and even for viewers that do support it, it may not be switched on all the time.
A PDF viewer that supports overprint preview, will mimick the effect of overlapping inks on screen; thus providing a realistic preview of how the PDF file would be printed on a decive which supports overprint. Read "How do I work with Overprint" for examples of applications supporting overprint preview (and how to enable it).
Why is this not enabled by default or available in all applications?
Unfortunately implementing proper overprint preview is not trivial. It's quicker and easier to treat all colors as knock-out, where they replace underlying colors, than to have to calculate how they would mix with underlying colors. Many viewers, such as Apple's Preview and most viewing applications on mobile devices choose not to implement overprint preview. As a result they should not be used to judge PDF quality or do proofing of PDF documents on screen.