IPA: /ˌɪnˈdɛlɪkɪt/
KK: /ɪnˈdɛlɪkɪt/
Not showing sensitivity or consideration for the feelings of others; lacking tact or good taste.
His indelicate remarks made everyone uncomfortable at the dinner party.
Indelicate is formed from "in-" (meaning not) and "delicate" (from Latin "delicatus", meaning pleasing or fine). The word describes something that is not fine or lacking in sensitivity or tact.
Think of 'not' ('in-') being combined with 'fine' or 'pleasing' ('delicate') — that's why indelicate means lacking in tact or sensitivity.