Most certainly means “without a doubt”, “absolutely”, “there is no question”. Basically, it's a way to say that what is being said is definitely true. See a translation.

What does it mean by most certainly?

Wiktionary. most certainlyinterjection. Used to indicate emphatic agreement.

Is most certainly correct?

Rest assured, the phrase most certainly is most certainly grammatically correct. Most simply adds emphasis to the adverb certainly, which is not an absolute word like unique, fatal, etc.