They are both considered synonyms in many literatures, yet there is a subtle difference ,when applying any of them .
'Meaning' is more concerned with what a word ,a phrase or an action directly conveys .
What is the meaning of the word "flower" in Spanish ?
You wouldn't say here ,what is the 'significance of it .
'Significance' is what a word , a phrase or anything could convey ,refer to in a more indirect way , a message that it could be communicating etc ..
What is the significance of this action ?
What is the significance of the word ( word x) in this particular context ?