The phrase "deep backstory" refers to a detailed and extensive history of a character or a situation. It includes important events, experiences, and factors that have shaped the character's personality or influenced the situation. Full definition
One reason we saved his reveal until now, in addition to him having a deeper backstory than the other new characters, is that Saw is an ally to the Rebel squad in Rogue One, but he's not really one of them. (ew.com)
Gard co-wrote the story for the games, giving Croft a deeper backstory and a more defined personality. (thewrap.com)
This deep backstory is seamlessly woven through present time. (bookbrowse.com)