What does sol solis mean?

Answer 1

Sol is the Latin word for "sun"; solis is its genitive (possessive) form. Latin nouns are often cited, and listed in dictionaries, using both of these forms, because knowing them allows you to derive all the possible forms of the noun (different forms are used in different grammatical circumstances).

There's also a certain online translation site that thinks that "sol solis" is a direct translation for the word "sun", but let's speak no more about that.