Tanya is the daughter of Castiel's former boss, Nora.
During his time as a human, Castiel worked at a Gas-N-Sip under Nora, his manager. Impressed by his work, Nora invited him to her house one night in what Castiel initially assumed was a date, but Nora wanted Castiel to babysit her daughter, Tanya.
Castiel was not confident in his abilities to care for the child, but when Tanya started crying in her crib, Castiel picked her up and sang her a song. When he tried to put her back in, Tanya cried again and Castiel resumed his singing.
When Tanya's temperature went up, Castiel panicked, only to learn from Nora that Tanya was okay, but the fact that Castiel panicked showed how much he cared about others.