A series of words working together to form a single adjective. If the phrase appears before the noun being modified, the words in the phrase are hyphenated in order to make the application of each word clear. The phrase so-called in My So-Called Life is one example.
To illustrate, compare the following sentences:
- DMan was a hot-headed noder who took a light-blue knapsack to the bus station.
- DMan was a hot headed noder who took a light blue knapsack to the bus station.
- The noder DMan was hot headed. He went to the bus station. He had a knapsack that was light blue.
In sentence (1), 'hot' modifies 'headed', and 'light' modifies 'blue', as intended.
In sentence (2) both hot and headed independently modify 'noder', and 'light' and 'blue' independently modify 'knapsack'. Thus DMan is 'hot' and 'headed' and his knapsack is 'light' and 'blue', all of which may (or may not) be true but deviate from our presumed intent.
In sentence (3) hypenation is not required because it is clear which words modify which other words.
Source: My recollection of The Chicago Manual of Style, and numerous recent Edit These E2 Titles requests which required a hypenation call.