Combining diacritics are unicode characters like accents or umlauts that, rather than standing on their own like other upstanding characters, combine with existing characters. There are plenty of unicode entities for common accented/modified characters (ç with a cedilla, è with an accent grave, ñ with a tilde, etc.), but not for every possible combination. (Plus, some less common combinations may not be available in every font; unicode is constantly being expanded, but not every system will have the most up-to-date support.) In cases where a specific accented character is required, but doesn’t actually exist in unicode, it can be built by specifying the base character, and then following it with a combining diacritic which adds an accent to whatever character precedes it.
For me, the situation where this most often arises is when I want to properly spell the name/title Spin̈al Tap with an n-diaeresis. Since there does not exist in unicode an “n” character with an umlaut, I put in a normal “n” and follow it with unicode character U+0308 (
̈). That allows me to satisfy my obsession with minor, unimportant details.
Some of you may be familiar with combining diacritics from the “Zalgo” internet meme, which creates a creepy effect by overdosing text with combining diacritics: