Wholly means completely, with nothing left over. A statement that is wholly false, a village wholly owned by one family, a decision wholly out of your hands.
It is the formal cousin of completely and entirely. You will meet it in contracts, court judgements and reports rather than in conversation: a wholly owned subsidiary, wholly dependent on aid, wholly unnecessary. It sits in front of adjectives and past participles, and it takes no object of its own. Not wholly is a quiet way of saying not quite — not wholly convinced, not wholly true. Two traps: it has two Ls, and it rhymes with holy, so it sounds like a word about saints and is nothing of the kind.
Wholly is whole with -ly on the end, and it reached modern English through Middle English forms like holly and holeliche. In those centuries it was a doublet of holy — the two words sat almost on top of each other on the page. Only later did the spelling of whole take its w, which is what keeps the pair apart today.
Middle English
holly
English, today
wholly
From Middle English holly, holeliche, holliche (also as halely, hallich, etc.). a doublet of - earlier a doublet of holy. by surface analysis, whol(e) + whole + ly.
Etymology from Wiktionary, CC BY-SA