You will almost only ever meet this reading inside two-syllable set phrases — overwhelmingly 的确 ('indeed') and the older transliteration 的卡 ('dacron / polyester'). Free-standing dí is not used in modern speech.
history
This is the oldest reading preserved on this character. In classical texts 的 meant 'bright, clear,' and from there developed the adverbial 'clearly, truly' sense kept alive today in 的确. Modern Mandarin handed the everyday workload to toneless de and shunted dí back into a few fossilised compounds.
Left white radical (Kangxi #106). On the dí reading the semantic link is unusually transparent: 白 'clear, bright' lines up with classical 的 'bright, evident,' the meaning that survives in 的确 ('clearly so'). Same indexing as 百, 皇, 皆.
Right phonetic 勺. The Middle Chinese reading was something like *tek, which fed all four modern readings of 的; dí is the closest survivor of that older sound. Same-phonetic family: 约, 钓, 灼, 酌. For the classical 'aim / target' use the dì page; for the modern grammar particle use the de page.
