Yuuri has just lost by a major landslide. He is a figure skater. He looks up to another figure skater named Viktor. Viktor, has no idea Yuuri even exists until Yuuri goes back to his hometown where he skates one of Viktor's routines perfectly.
Viktor then decides to go from Russia to Japan to be Yuuri's coach.
Yuri on Ice focuses on Viktor and Yuuri's relationship with each other, with a lot of figure skating mixed in between. It has lovable characters, and it breaks gender roles. (To some extent)
But it really focuses on Viktor and Yuuri.