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.
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. Packages for setting man pages support example displays but not keeps.
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”. A floating keep might appear at the bottom of the current page if it fits, and at the top of the next otherwise. Alternatively, it might be deferred to the end of a section. Use of a floating keep can prevent a large vertical space from appearing before a tall keep of the ordinary sort when it won’t fit on the page.