Hi Luke,
Generally it’s used when you’re talking about “the ___ one”, eg:
紅色的 the red one
桌子上的 the one on the table
我媽媽的 my mum’s
But it was also be used optionally where it would also be correct to omit it. This comes with feel and alters your tone slightly, eg:
他的眼睛還蠻大的 His eyes are quite big
我覺得她人還蠻好的 I think she’s quite nice
他挺那個的 He quite y’know (it’s obvious from the context what you mean here)
Hope that helps
Laurence