Acritarchs are mysterious microfossils found in large quantities in strata dating from 2.1 billion to 400 million years ago. For reference, complex multicellular organisms appeared about 600 million years ago, but didn't really take off until the "Cambrian explosion" some 540 million years ago. Essentially, any small, decay-resistant, non acid-soluble bit of organic material from Proterozoic (2500 - 542 million years ago) strata is categorized as an acritarch. Most acritarchs are interpreted as the fossilized remains of resting cysts of green algae or other eukaryotes (complex-celled organisms), formed when the organism is somehow under duress and needs to go into hibernation for a while. In the case of these fossils, "a while" turned out to be forever. Some acritarchs may also be early embryos.
Acritarchs are important to studies of the early history of life on Earth because they're among the only fossils that date before the Ediacaran period (which began 635 million years ago), when the only life on Earth is presumed to have been unicellular. The acritarchs are by definition all they really left behind. Acritarchs are mostly remnants left by eukaryotic organisms, rather than bacteria, which are about ten times smaller.
The first known acritarch, Grypania, appears in the fossil record about 2.1 billion years ago. These tiny tube-shaped fossils are among the oldest known, with some of them reaching a centimeter in size, colossal for a time when the average organism was about 10,000 - 1,000,000 times smaller. There is uncertainty over whether Grypania was a large bacterium, a bacterial colony, or an early algae (eukaryote), but its size and consistent form have caused most paleontologists to label it an algae.
Besides Grypania, most of the earliest acritarchs are simple and spherical. Powerful microscopes have done little to reveal their secrets, as most nano-scale organization has been lost over the hundreds of millions of years. From 2 to 1 billion years ago, the diversity of acritarchs increases, and examples are found with various surface ornamentations, such as bulb-shaped vesicles, spikes (which would have repelled predators), triangular, funnel-tipped, or hair like protrusions, and other features. These acritarchs provide some of the earliest evidence of the existence of predation and the diversification of early eukaryotic life.