So, the play goes down during the seventh year of the Trojan War. You know, that epic war that gave us the model of Western "heroism" and a ton of great literature (like Homer's Iliad and Virgil's Aeneid) .
Does that mean that Shakespeare's play follows in the footsteps of Homer? Well, don't go getting your hopes up. Shakespeare's version of the Trojan War is totally cynical and calls into question everything Homer writes about it in the Iliad. In Troilus and Cressida, the battlefields are full of dishonorable acts, despite all the soldiers' big talk about "honor" and performing "magnanimous deeds." The war itself, we're reminded, is fought for a completely foolish reason. (Because Paris stole Helen from Menelaus.)
So, if the Trojan War is supposed to be the "founding event" of Western civilization and Shakespeare turns that event into a brutal joke, then what is this play trying to tell us about Western civilization in general? That Western civilization itself is a brutal joke?
Gee. It's no wonder the play wasn't very popular in Shakespeare's time. See, the Elizabethans considered the story of Troy and the Trojans a major part of their nation's history and identity. Basically, they thought of Troy as the birthplace of the British nation because they traced their history back to Brutus (a.k.a. Aeneas's great grandson).
According to tradition, Aeneas is the famous dude who high-tailed it out of burning Troy and went to Rome in Virgil's Aeneid. Well, his grandson Brutus had a boatload of followers called "Britons" and around 1074 CE, they showed up on a little island called Albion and named their most important city Troia Newydd (New Troy). Eventually, New Troy was renamed Londinium (a.k.a. what we now know as London) (source).