Maine and Nebraska award their electoral college votes to the winners of each congressional district. That's two votes to the statewide winner (Senate seats are statewide and there are two per state). And one vote for each House district.
ME-01 means the first congressional (House) district of Maine. The voters there voted for Hillary Clinton. ME-02 is the second congressional district of Maine. Those voters voted for Donald Trump. Overall, Maine voted for Clinton, so she received three votes, one for ME-01 and two for the state. By convention, they only mention explicitly the vote that does not align with the statewide vote.
In 2008, the same thing happened with NE-02 which is the Nebraskan district for Omaha. Barack Obama won the urban district but lost the other two.
ME and NE are the postal codes for Maine and Nebraska respectively. They just happen to be similar. Using the postal codes with two digits is a common way to represent congressional districts. If you see something like WY-AL, that means that the state (e.g. Wyoming) has just one at-large congressional district.