Aspidella are believed to be fossils of organisms which lived in watery environments around 600 million years ago.
They are found in shale and slate deposits, and are small (1 - 180mm diameter ) disc shaped indentations with prominent star-like ridges.
They were first described in 1872 after findings in Newfoundland. At the time, many geologists thought that they were inorganic in nature - perhaps the imprints of gas-escape bubbles.
Modern-day opinions lean towards the idea they may have been jellyfish-like organisms - or possibly anemone-like.
Note that some fossils have recently been suggested to show possible movement 'trails' - ref.
More info. see: Wikipedia