What is filio in latin?

It's a form of the Word filius, meaning "son." If it appears by itself, it's probably dative and means "to or for a son." The ablative singular takes the same form, but usually appears after a preposition, as in the following phrases:

cum filio "with a son"

a filio "by a son"

de filio "about a son"

Latin has no articles. so in any of these translations you could replace "a" with "the" (or even, depending on context, "his" or "her").