A font typically defines shapes for a single alphabet or script. Therefore, displaying the entire range of scripts that Emacs supports requires a collection of many fonts. In Emacs, such a collection is called a fontset. A fontset is defined by a list of font specs, each assigned to handle a range of character codes, and may fall back on another fontset for characters which are not covered by the fonts it specifies.
Each fontset has a name, like a font. However, while fonts are stored in the system and the available font names are defined by the system, fontsets are defined within Emacs itself. Once you have defined a fontset, you can use it within Emacs by specifying its name, anywhere that you could use a single font. Of course, Emacs fontsets can use only the fonts that the system supports; if certain characters appear on the screen as hollow boxes, this means that the fontset in use for them has no font for those characters.1
Emacs creates three fontsets automatically: the standard fontset, the startup fontset and the default fontset. The default fontset is most likely to have fonts for a wide variety of non-ASCII characters and is the default fallback for the other two fontsets, and if you set a default font rather than fontset. However it does not specify font family names, so results can be somewhat random if you use it directly. You can specify use of a specific fontset with the ‘-fn’ option. For example,
emacs -fn fontset-standard
You can also specify a fontset with the ‘Font’ resource (see X Resources).
If no fontset is specified for use, then Emacs uses an ASCII font, with ‘fontset-default’ as a fallback for characters the font does not cover. The standard fontset is only used if explicitly requested, despite its name.
A fontset does not necessarily specify a font for every character code. If a fontset specifies no font for a certain character, or if it specifies a font that does not exist on your system, then it cannot display that character properly. It will display that character as an empty box instead.
[1] The Emacs installation instructions have information on additional font support.