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Display fonts are fonts primarily designed to be used in "display" (headlines, titles and so forth) rather than for long-distance text.
Like most categorisations of type, the category of "display" fonts is flexible. Some fonts are "display" fonts because they are flamboyant or quirky, typographical peacocks; but careful designers and foundries will often produce "display" versions of text fonts, which are likely to be just as sober as the text font, but are designed to be used at large sizes. Such versions are likely to feature adjustments to x-height, stroke weight and letterfitting which help them look and read their best at larger sizes.
As a general rule, display fonts are best used for larger settings, such as headlines and titles. They can also be used for short paragraphs where immersive or lengthy reading is not required.
For better readability, long-running copy for such things as brochures, magazines and web sites use a text font.