A blockchain is a distributed network of computers that all have a full copy of a ledger (think debit, credit, total). Blockchain technology is incredibly secure and is "trustless" when implemented in a public way, that is, it does not give trust to a central authority. Therefore voters can be assured that when they cast their vote, their vote is immutable. In a public blockchain results are near-real time and publicly viewable (think Voter1234 voted for Candidate 1).
This technology is the first that could allow online voting in a secure and efficient manner. This technology could apply to many other government functions (e.g. city council voting, titles, licenses, etc.) as well. Such systems could significantly reduce the cost of voting board activities, improve the "customer experience" of citizens/businesses/government leadership, and provide the security/transparency in voting that many seek. This technology could also benefit the environment by reduction or elimination of paper ballots and reduction or elimination of gas spent driving to polling places.