DID I use the word "significance" correctly? (not Do)

it's correct but I would probably use "importance" instead of "significance" . we need more context to say whether or not "significance" should be used.

There's nothing wrong with the way you used significance here. However, apart from more formal and academic writing, significance isn't used that much. Instead, you can use benefits or importance which would have a similar meaning depending on exactly what you want to say. For example, benefits would focus on benefits eating less meat will have on the person as well as on the environment whereas importance would focus on how important eating less meat is: less factory farming and returning the balance to the natural system.

It's quite hard to give a definite answer to this question without a bit more information...can you explain what you mean by 'significance' in this example using different/more words