Be honest: the first thing that went through your head was "what the hell", right?
Thought so.
As Yu Darvish demonstrated for us above (at 55 mph), the eephus pitch is an off-speed junkball. It is thrown with low velocity, and a high arc similar to a slow-pitch softball pitch. It's not always thrown for a strike, although it ideally should catch the hitter off-guard and end up in the strike zone.
The pitch's invention is credited to Rip Sewell, a former pitcher who played from 1932 to 1949. Sewell had injured himself in a hunting accident in December 1941, which necessitated a change in his pitching delivery. This change led to Sewell messing around with his pitches and eventually throwing one by holding onto the seam and using three fingers during the release to create backspin. Sewell threw the pitch for the first time in an exhibition game, and subsequently incorporated it into his repertoire. The eephus pitch, named by Pittsburgh outfielder Maurice Van Robays, helped Sewell become one of baseball's best pitchers of that era. During the 1946 All-Star Game, he threw the eephus to Red Sox slugger Ted Williams several times, before Williams finally connected and knocked the ball out of the park: the only home run ever hit off of Sewell's eephus pitch. So... who else has thrown the pitch? Quite a few pitchers (aside from Sewell and Darvish) have used the eephus at some point during their careers, and a couple of them may surprise you:
• Pedro Borbón
• Casey Fossum
• Steve Hamilton
• Liván Hernández
• Phil Niekro
• Orlando Hernandez
• Bill Lee
• Vincente Padilla
• Satchel Paige
• Pascual Perez
• Kazuhito Tadano
• Carlos Villanueva
Now... raise your hand if you think you'd strike out on an eephus pitch.