Other forms: hyphenations
Hyphenation is what you do when you use a dash-like punctuation mark to join two words into one or separate the syllables of a word. See the word dash-like in that previous sentence? It's formed using hyphenation.
The process of using a hyphen, that short dash in compound words like dog-friendly, fast-acting, and well-known, is what hyphenation is all about. We also use hyphenation when we're writing and need to split a long word between lines, breaking it in half and adding a hyphen between complete syllables. The Greek root is hyphen, "mark joining two syllables or words."