Stannis Baratheon tried to take Winterfell from Ramsay Bolton. Occupanying his army were his queen and his daughter. The red woman convinced Stannis to sacrifice his daughter (burn her alive) in order to win the coming battle. Little pincess Shireen dies screaming, the queen hanged herself the next morning, and Stannis lost the battle anyway.
The toy that Davos found belonged to Shireen. The burned wood by his feet was the remnants of the burning.
Not sure what deeper meaning the show was trying to make.
Slightly different topic:
The Red Lady is a priestess of the Lord of Light. In a few cases, such people have been able to bring people back from the dead. Jon was dead. She brought him back to life. He was asking her not to do that again.
Can you watch the previews for next week? Davos figured out that the stack of wood was actually a pyre and his favorite little princess is mixed in with the ashes. They show exactly where that’s going next week. Only if you want to know...
The carved Stag (Baratheon sigil) was a gift from Davos to Shireen before he left. Stannis had sent him on some mission, probably because he knew Davos would stop him from burning his young daughter to death. Davos had a soft spot in his heart for Shireen, the young girl who taught him to read.