Is it a euphemism for plants someone views as being comparable to excrement? Not at all. Green manure is a valuable resource closely related to green mulch.
While there are plenty of contexts in which manure is not desirable, it is good in the garden: it is an excellent fertilizer, providing the nutrients plants need, while not involving any of the environmentally-harmful industrial production processes associated with artificial fertilizer. It is this positive aspect of manure that the phrase green manure refers to.
But what exactly is green manure? Quite simply, it is plants that have been uprooted and lain on or plowed into the soil. Essentially, it is the practice of composting in place. Instead of pulling plants, bringing them to a compost pile, waiting for them to break down, and then carrying the resulting compost back into the garden, the organic material is simply placed where the compost is wanted, to gradually break down and return its nutrients to the soil.
That is, of course, how the process works. Plants are made out of exactly the stuff that other plants need (even more so than animal droppings), and when a plant is no longer alive to hoard and use those resources, it passes them on to other plants. Thus, green manure is the perfect fertilizer in terms of its effectiveness in providing nutrients to plants – as well as being cheap, abundant, and readily available without the need for manufacturing or transportation.
Pretty much any plant can be used for green manure. We can cut down the stems of plants that have died back (after insects are done overwintering in them) and use those as green manure. We can pull weeds and use them as green manure (though we should take care to educate ourselves about which species will simply take this as an opportunity to spread themselves around more). Or we can cultivate plants that are especially good at being green manure.
Two characteristics make a plant suited to this role in the garden. First, the plant must either spread rapidly – so the gardener can harvest some individuals for green manure and still have plenty of living plants to continue reproducing themselves – or the plant must regrow rapidly, so that it can survive having its leaves harvested on a regular basis. (When a gardener cuts down a plant, uses the leaves and stems for green manure, lets the plant regrow, and then harvests it again, that’s called chop and drop.) Second, a great green manure plant is a dynamic accumulator.
What is a dynamic accumulator? All plants pull nutrients from the soil and incorporate them into their bodies. But some plants are especially good at finding and absorbing nutrients. When these plants are used as green manure, they are similarly talented at making nutrients available to the next generation of plants.
As one example, many permaculture practitioners cultivate a plant called comfrey for its value as green manure, as well as its many other uses. Comfrey is not native to North America, though, so those who strive to be native plant purists may prefer to find another species to provide this valuable function.