Displays are sections of text set off from the surrounding material (typically paragraphs), often differing in indentation, and/or spacing. Tables, block quotations, and figures are displayed. Equations and code examples, when not much shorter than an output line, often are. Lists may or may not be. Packages for setting man pages support example displays but not keeps.
A keep is a group of output lines, often a display, that is formatted on a single page if possible; it causes a page break to happen early so as to not interrupt the kept material.
Floating keeps can move, or “float”, relative to the text around them in the input. They are useful for displays that are captioned and referred to by name, as with “See figure 3”. Depending on the package, a floating keep appears at the bottom of the current page if it fits, and at the top of the next otherwise. Alternatively, floating keeps might be deferred to the end of a section. Using a floating keep can avoid the large vertical spaces that may precede a tall keep of the ordinary sort when it won’t fit on the page.