IPA: /ˌɪn.səˈprɛs.ə.bəl/
KK: /ɪnˈsʌprɛsəbl/
Something that cannot be controlled or held back; it is unstoppable or cannot be suppressed.
Her insuppressible laughter filled the room, making everyone smile.
Insuppressible is formed from "in-" (meaning not) and "suppressible" (from the Latin "suppressus", meaning to press down). The word describes something that cannot be pressed down or contained.
Think of something that cannot be 'pressed down' ('suppressible') — the 'in-' means not, so insuppressible means it cannot be contained.