IPA: /ɪnˈɛksplɪkəblɪ/
KK: /ɪnˈɛkspɪkləblɪ/
In a way that cannot be explained or understood.
The lights turned on inexplicably in the middle of the night.
Inexplicably → It is formed from "in-" (meaning not) and "explicare" (meaning to explain) combined with the suffix "-ly" (meaning in a manner). The word "inexplicably" means in a manner that cannot be explained or is not explainable.
Think of 'not' ('in-') being combined with 'to explain' ('explicare') — that's why inexplicably means something that cannot be explained.