A day that a typical high schooljunior enrolled in several AP classes experiences daily. Possibly as a result of an unannounced English paper, a monotonous Chemistry lesson about god knows what, a lecture be the rotund physics teacher, a ridiculous calculus test, the simple presence of a Latin or Spanish class, or most likely, a combination of at least 3 of the above.
Chem Teacher: Let's begin!
Dennis: Ughh, I'm not ready for this, it's just been that kind of day.
Stephen: Don't tell me we have a physics test!
Dan: Yeah that homo laid it on thick today!
Stephen: Well what can you expect, it's just been that kind of day.
Xander: What's that smell!?! (looks at shoe and sees he stepped in dog shit) Figures, it's just been that kind of day.
Used as a response to point out an unintentional double-entendre in which the original speaker could be taken as intending to perform some act that would be more appropriate for a sex, kink, or other "special" party.
Person A: I'm going down to get a drink of lemonade, do you want some?
Person B: Dude, it's not that kind of party!
Person A: "Hey, I'm going out to eat. Wanna come?"
Person B: "Sure, why not?"
Person A: "Alright."
Person B: "Um, could you buy my food?"
Person A: "...it ain't that kind of party."