Slang coined by the Umamusume fanbase, deriving from the title and song lyrics of the Umapyoi Densetsu song. Generally used in the sense of: 1. To finish a given horse girl's training scenario in the Umamusume game; 2. To get along very well or "buddy buddy" with a given girl (or Kiryuin Aoi); or 3. To "go all the way" or do all sorts of implied hanky panky things with a given girl (or again, Kiryuin Aoi).
Effectively used as a euphemism in most fan comics, especially in 'comedic' scenarios, where it usually involves a girl going yandere on the Trainer and alleging the latter umapyoi-ing the other girls. Occasionally it is Happy Meek accusing Kiryuin Aoi (of going out with the Trainer), as a reference to one of the in-game events.
A common variation used by fans (but not in official media) is "onsen umapyoi", occasionally abbreviated to "onsenpyoi" (温泉ぴょい). This can refer to either: 1. to finish a given horse girl's training scenario with the semi-secret hot spring event unlocked, which requires the player to randomly acquire the Hot Spring Tickets in that scenario and win the URA final, or 2. from the above, to "go all the way" at the hot spring ryokan with a given girl (or, yet again, Kiryuin Aoi).
Since the release of the Aoharu training mode, Kashimoto Riko has joined Kiryuin Aoi in the list of possible umapyoi-ees (or, alternatively, umapyoi-ers).
The song also features other 'nonsensical' portmanteau words such as umadacchi, sukidacchi and umapoi (without the 'y'), all of which are also co-opted by the fanbase for pretty much the same meanings as umapyoi above. As such, these examples can also be tagged umapyoi.
Usage of all these four words has also spread to other fanbases.
This tag should generally not be used when the words occur as part of the Umapyoi Densetsu song, i.e. the characters are singing the song normally in their original context.
Variations
うまぴょい umapyoi, "horseyhop!"
うまだっち umadacchi, "horseypals!" or "horsey-stand-up!"
