Cordyceps are a family of mushroom which consume insects and larvae. Due to the complex and dense nutritional nature of insects they provide a fantastic food source for the fungus to grow from. As a result they create unique polysaccharides which have shown benefits to human health.
The most understood Cordyceps is called 'Cordyceps Sinensis', there are many research papers and studies on this fungus.

The compounds found in Cordyceps have many effects on the human body. Oral consumption can increase blood flow around the body, as well as elevating cellular energy levels and ATP efficiency.
The above effects can enhance healing (cellular repair), lift mood, fight fatigue and act as a sexual stimulant.
Cordyceps can also protect and promote regrowth of nerve cells.
Ergosterol, present in Cordyceps, is converted into Vitamin D2 within the body which acts as an anti-viral and anti-arrythmic.
There are many other health benefits to consuming cordyceps as a supplement, please consult the various peer-reviewed studies available on NCBI and Google Scholar.

Until recently not much was understood about the native Australian 'Cordyceps Gunnii". We have had our specimens analysed by Aloha Labs in United States, analysis showed very similar composition to C.Sinensis.
Additionally composition analysis has been performed in the Engineering Research Center of Industrial Microbiology, China. This confirms that all active compounds from c.sinensis are also present in c.gunnii.
These comparisons are available in the photo section.

A Systematic Review of the Mysterious Caterpillar Fungus
Traditional uses and medicinal potential of Cordyceps
Anti-influenza effect of Cordyceps through immunomodulation

We always recommend people perform their own research and build an understanding of any natural medicines, there is a lot of information available on scholar.google.com