Incorrect spelling, explanation: some users of English believe that when they form an adverb from the adjective local, it is enough to add just -y to the word as the -l letter is already there. However, the rule of forming adverbs from adjectives is by adding -ly to an adjective. Therefore, you need to double the -l letter as the form localy is incorrect.

Correct spelling, explanation: the adverb locally and the adjective local have their origins in the Latin word locus and it used to mean a spot or place, which is close to the contemporary meaning. The word locally needs a double -l, as it is an adverb and the basic rule of forming this part of speech, is to add an -ly ending to an adjective. In this particular case, the adjective ends with -l so as a result, we need a double.

Definition of locally:
1. adverb – refers to something that occurs in a close surrounding or in a particular area,
In our restaurant, we use the highest quality ingredients, grown and produced locally.

Expressions with locally:
The word usually appears as a part of collocations with past participles verbs, such as locally produced, locally made, locally grown,
The most delicious vegetables and fruit are grown locally as they don’t contain any chemicals or artificial additives.