Correct spelling, explanation: summary has its roots in the Latin word summa, meaning total, and this origin is also why the word has to keep the double m. Another reason is the pronunciation, as the double m, in a way, binds the word together and makes the pronunciation more intuitive for the reader.

Definition of summary:
noun
1. a statement covering the most important parts of something
When I study I like to make a summary of all information learned in a given lesson.
adjective
1. only including the most important information
The management held a summary meeting in which we had to shortly present what we’d achieved in a month.

Incorrect spelling, explanation: sumary is an incorrect word because it noticeably differs from the root word, which in this case is Latin summa. In general, as long as there is no good reason to change the structure of the word, they stay unchanged, and there is no good explanation as to why one m of summary should disappear.