The Legend of Korra's brooding firebender Mako dated both Korra and Asami (with a little overlap), but the series ends with Korra and Asami falling in love with one another and running away for a romantic vacation in the spirit world. Their relationship was left somewhat ambiguous in the actual show, with Korra and Asami simply holding hands and facing one another, but co-creator Bryan Konietzko posted a statement confirming "Korrasami is canon" a couple of days after the finale aired.
In his statement on Tumblr, Konietzko explained that he'd first started to bring up the idea of Korra and Asami getting together in the writers room during season 1. At first it wasn't discussed seriously, since they didn't think it was something they would be allowed to do in an animated show for a kids network. When Konietzko and co-creator Michael Dante DiMartino finally approached Nickelodeon with the proposal, the network was "supportive" but said "there was a limit to how far we could go with it," which is why Korra and Asami don't kiss in the show.
They do kiss, however, in the Legend of Korra sequel comic "Turf Wars," which confirmed their relationship and saw them coming out to their family and friends - including Mako. Korra and Asami's ex-boyfriend finds out they're together when the two embrace and kiss after a battle with the Triple Threat Triad outside Republic City's new spirit portal. Mako is definitely stunned by the news and is somewhat awkward in telling them it's "cool" at first.
"Turf Wars" also details cultural attitudes towards same-sex relationship in the Four Nations. The Air Nomads are the only tribe that are completely open and accepting of all orientations. The Water Tribes are also fairly accepting, but people are expected to be discreet about same-sex feelings or relationships. The Earth Kingdom is more repressed, and same-sex relationships are considered taboo there. Meanwhile, Fire Lord Sozin outright made same-sex relationships illegal in the Fire Nation and the parts of the world that it conquered.
Later in "Turf Wars," after Asami has been kidnapped by the Triple Threats, Mako approaches a worried Korra to comfort her. When the two of them are finally alone, he explains, "If you've noticed me acting a little weird, it's only because I've never had one of my exes date another one of my exes before." Ultimately, though, Mako is very supportive of Korra and Asami's new relationship, telling Korra, "I think you... are both perfect for each other. And I'm the most qualified person to say that."