That was due to two reasons - proximity to Finland and Sweden combined with political leadership that recognised the absolute need to become a leader in that area.
The second part I agree with, but not with the proximity to Scandinavia argument:
- In the 1990, the Estonian banks introduced online services that were ahead of anything in the West, including Scandinavia.
- Estonia became the first nation to hold legally binding general elections over the Internet with their pilot project for the municipal elections in 2005. The Estonian parliamentary election, 2007, also used internet voting, another world first.
- In 2003, Skype, a voice-over-ip service and software application, was developed technically by Estonians Ahti Heinla, Priit Kasesalu and Jaan Tallinn, who were also behind the Kazaa peer-to-peer file-sharing software.
- In 2007, Estonia made international headlines by becoming the first country in history to successfully
defend itself against a large-scale cyber attack (from Russia). A positive outcome of this event was that
Estonia's capital, Tallinn, became the home of the NATO Cooperative Cyber Defence Centre of Excellence in 2008. Etc.
I think it shows that it was Scandinavia following Estonia rather than the other way around. More here:
ericsson.com/res/thecompany/docs/publications/business-review/2012/issue2/life_in_e-stonia.pdf