The yellow drumheads of young fungi and the white 'eggs" of mature ones make it easy to identify. Fluted bird's nest (Cyathus striatus) has grooves inside the nest, and dark grey eggs.
The "eggs" are called periodoles and contain the spores. Each is attached to the nest by a cord called the funiculus. When rain falls into the cup, the periodoles are splashed out and the funiculus breaks. The frayed funiculus is sticky -- as is the periodole -- so they generally gom onto something as they fly away. What happens next is not clear, since finding escaped periodoles in the wild is a daunting task, but eventually the spores are released from the periodole and infect woody debris.