These little gems are bird's nest fungi, with 5 genera in the Nidulariaceae family. They are saprophytic, feeding on dead wood and wood chips, helping the gradual transition toward soil.
Wikipedia has extensive technical information but for my purposes, Mushroomexpert.com explains them best.
"These odd and fascinating little fungi look for all the world like tiny birds' nests. The fruiting bodies form little cuplike nests which contain spore-filled eggs. The nests are called "peridia" ("peridium" in the singular), and serve as splash cups; when raindrops strike the nest, the eggs (called "periodoles") are projected into the air, and they latch onto twigs, branches, leaves, and so on. What exactly happens next is not completely clear, but eventually the spores are dispersed from the egg. They then germinate and create mycelia, which eventually hook up with other mycelia and produce more fruiting bodies."*Gala's picture shows the distinctive fluted bird's nest fungus, Cyathus striatus, which is wide spread in temperate regions. It is distinguished by hairiness and the grooves in the cup wall, resembling the paper around a cupcake. In our urban setting it is commonly found in wood mulched garden beds.
A mushroom is the "flowering" part of a fungus, intent on getting its spores up in the air where they can be dispersed by the wind. Many mushrooms have their spores below an elevated cap where they can fall downward. In this case, when the egg is propelled into the air by the impact of raindrops, it rips open the funiculus and a tightly wound funicular cord spirals off like a spinning reel in free fall. The sticky cord clings to a nearby plant or blade of grass, dangling the egg like a tetherball. Its spores are then hanging up where the wind can carry them away.
* Mushroomexpert.com has an identification key.
Time lapse video from Cornell shows them emerging.