In preparation for last night's titular "The Battle of the Bastards," Davos took himself for a long walk in the fields around where the Stark camp was set up, to calm his nerves and think. And to poo in private. While he was out there, he stumbled upon a snow-covered pile of wood with a suspiciously familiar item amongst its rubble. Though Davos' realization about the pyre will have to wait until next week to be carried out further, the pieces he put together there will certainly provide motivation for Davos going forward. So what did Davos find at the pyre?
The item Davos pulled from the wreckage was just intact enough to be recognizable: it was the small figure of a stag made out of wood, a child's toy. The toy of a specific child, in fact, and a toy that was made by Davos' own hand. It was a gift from him to the late Shireen Baratheon, whose fate Davos hadn't known until the evidence was staring him in the face. The fact that Shireen's stag lay in the pyre revealed to Davos the gruesome events from the end of Season 5, when Shireen was burned alive by Stannis and Melisandre.
It's unclear why Davos didn't do more investigating into Shireen's fate before now. He tried to ask Melisandre once, but they were interrupted; it's possible he just assumed Shireen's death was much less violent than it actually was. Now that he does know, however, he's probably going to be bringing some inquiries Melisandre's way soon. Davos' relationship with Shireen was one of the most heartfelt on the show, filled with a genuine kindness not often seen in the world of Westeros. Shireen was a gentle and good person who didn't deserve the death she endured (not that anyone really deserves to be burned alive), and Davos is bound to be hit particularly hard by the realization of what happened to her.
Shireen's death was orchestrated and carried out by Melisandre in a R'hllor-sponsored attempt to magically clear the way for Stannis' soldiers. Though the snow did melt and allow the army to move, it all ended up being for naught. Many horrified soldiers deserted and Stannis' remaining army was slaughtered by the Boltons, with Brienne stopping by just in time to end Stannis herself. Losing the battle made Shireen's death even more senseless than it already was.
Going forward, Davos' plans are unclear. He could seek some kind of vengeance against Melisandre, despite their tentative team-up to resurrect Jon. The Starks may have won for now, but that victory is new and tentative; there are a lot of unknowns left to be dealt with. The last thing Team Stark needs is dissent amongst the ranks, but these are extenuating circumstances. If Davos decided to take some kind of action against Melisandre for what happened to Shireen, who could blame him?