Publication bias occurs when some studies are published and others are not. Studies that remain unpublished tend to be systematically different from those that are published, meaning that conclusions drawn from the published literature will be systematically different from the truth (or biased). Positive trials and “exciting trials” are more likely to be published. Sometimes publication bias is nefarious: companies selling medications have a vested interest in hiding negative trials about their products. However, publication bias can also occur because researchers don’t think their results are interesting, or because journals are less interested in publishing negative or “boring” research results.
Registering trial protocols before they start, such as with a website like clinicaltrials.gov, is meant to combat publication bias.
AllTrials is an initiative to aiming to ensure that all research results or registered and published. You can sign their petition or donate to their cause on the website.
Publication bias is a type of reporting bias.
For a great book that covers this topic, check out Bad Pharma by Ben Goldacre.