I don't get it, what the hell is this
They're making a reference to the webcomic Homestuck.
In Homestuck the majority of the characters are aliens who are culturally different. A major part of their culture is that they have 4 different romances. These romances are also heavily base on media trends.
Hearts: Basically the closest to human romance.
Diamonds: Confidant, bromance, blood brothers. Take your pick.
Spades: Foeyay, enemies with a lot of sexual tension. Think Batman and Joker if they actually fucked. (Also maybe if they never crippled any bystander to their fights).
Clubs: the one that's most socially okay to have a fling with and the only one that has 3 people instead of 2. This one is actually the last explored and so we know the least about. Often described as 2 people disagreeing with a 3rd person mediating between them so they don't murder each other. Personally I always saw it as the power trio trope. Y'know Kirk-Spock-Mccoy. The ultimate goal is that mediator suffers through their disagreements to ensure the best outcome.
Actually now that I think about it Tomoko x Komiyama being mediated by Yuu would also fit the club ship.
That's as basic as I can get without going into detail.