Correct spelling, explanation: the spelling of the word luxury is based on the original Latin word luxus. In English, the word has gained the suffix -ry, which signifies the state or character of something. Besides that, the internal structure of the original word has not been changed too much. The spelling of luxury is a little different than luxus, but the similarity is still very noticeable.

Definition of luxury:
noun
1. a state of comfort, often associated with wealth
Everyone dreams of luxury and riches.
Not everyone has the luxury to work from home for good money.

Incorrect spelling, explanation: luxary is an incorrect word because it does not fit the original Latin word used to create it – luxus. Sometimes vowels change in the process of adapting a word to another language or to simplify it, but in this case, the u in luxus stayed the same in luxury, and it’s the spelling that changed and became more anglicized due to speakers’ convenience.