To convert into or treat as an adverb; to give adverbial function or quality to a word or phrase.
From 'adverbial' (adjective) + '-ize' (suffix creating verbs, from Greek '-izein'). The '-ize' suffix is productive in English for creating verbs meaning 'to make' or 'to convert into.'
The '-ize' suffix is so productive that English speakers can theoretically create verbs from almost any noun or adjective—'adverbialize,' 'marginalize,' 'weaponize'—though not all such coinages become established words. It shows English's incredible flexibility in creating new verbs on the fly.
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