I'm not too sure, but from their leaflet I get the impression that there isn't much, unless you work/study/visit there:
As an e-resident you can use and enjoy the same great digital services that allow Estonians
to do anything and everything digitally–sign all documents, launch and manage companies, do the banking, encrypt files, etc. For a closer look on how the digital way of life goes in Estonia: http://e-estonia.com/. It is especially useful for entrepreneurs and others who already have some relationship to Estonia: who do business, work, study or visit here but have not become a resident. However, e-residency is also launched as a platform to offer digital services to a global audience with no prior Estonian affiliation – for anybody who wants to run their business and life
in the most convenient aka digital way!