IPA: /ˌɪn.dɪˈzɒl.jʊ.bəl/
KK: /ɪnˈdɪsəˌluːbəl/
Something that cannot be broken, dissolved, or undone; it is permanent and binding.
Their friendship was indissoluble, lasting through all challenges.
Indissoluble is formed from "in-" (meaning not) and "dissolubilis" (from Latin "dissolubere", meaning to dissolve). The word describes something that cannot be dissolved or broken apart.
Think of something that is 'not' ('in-') able to be 'dissolved' ('dissolubilis') — that's why indissoluble means it cannot be broken apart.