In The Mandalorian, the term foundling is first used in "Chapter 1: The Mandalorian." As the show delves into Mando's history, the series uses foundling to refer to younger members of the Mandalore's culture, with Mando saying "I was once a foundling," followed by flashes of a young Din Djarin hiding in a war zone — right before he is rescued by the Mandalorians.

Foundlings are abandoned or helpless children who, when encountered by a Mandalorian warrior, are taken in and raised by them. Like others before him, Mando was a foundling brought into Mandalore culture and trained to be a capable warrior, and it's clear that the Mandalorians hold foundlings in high regard. What Mando doesn't realize until "Chapter 8: Redemption" is that, through his actions to protect Grogu, he has taken the child on as his own foundling. As Moff Gideon comes looking for Grogu, the Armorer (Emily Swallow) explicitly tells Mando that Grogu "is a foundling [...] By Creed, until it is of age or reunited with its own kind, you are as its father." By taking in a foundling, Mando also earns his Signet and the right to start his own clan. 

In Mandalorian culture, taking in foundlings continues their way of life, and is a huge step in a Mandalorian's journey. 

At the end of "Chapter 14: The Tragedy," Mando has lost his foundling to Moff Gideon, and he must get him back, both for his personal honor and to save Grogu, who he clearly cares about.