This narrative or style commonly imagines an alternate history where widely available cheap (or free), clean, and often highly portable electrical energy replaces all previous energy sources (such as wood, coal and oil, and the steam engines that were fueled by them), but has yet to be replaced (or is never replaced) by other energy sources itself (such as diesel or atomic power).
Seems fairly straightforward. Clean energy sources. But how many can you name? Clean-energy-ideas.com lists the merits of clean energy such as: solar power, wind, hydro, and geothermal energy. Creating a world relying on these instead of gasoline doesn't seem so far-fetched. In fact, it seems practically utopian.
Teslapunk was named after scientist and inventor Nikola Tesla. Who was he? Tesla was, unsurprisingly, a pioneer in developing electricity. He also dreamed of creating an airplane without propellers or engines, working by a series of electromechanical ground stations or an on-board energy source. Have you heard of Tesla's "peace ray"? Back in the early 1900s, Tesla created an electrical weapon which was dubbed a "peace ray" or death ray by the media.
If you want to learn more about Tesla and his radical ideas, try the Wikipedia page.