What significance does the number 26 have in anime?

Because 13 episodes is the standard number for a "full season" of any given television program. If you'll notice, in both Trigun and Cowboy Bebop, the 13th episodes signify a sort of closure, or a heightening of circumstances in the plot of the series. Episode 13 of Trigun is titled "Vash The Stampede" and the entire episode is a big series of flashbacks followed by one huge character revelation at the end. Episode 13 of Cowboy bebop is the 2nd part of the "Jupiter Jazz" two parter. It signifies the end of the "first season" of the show, leaving the viewer with a ton of stuff to look forward to in the next season. That answer your question?