Meanings
According to some, the expression originally literally referred to greeting someone with the obsolete greeting "good time of day", or other greeting appropriate to the time of day (e.g., good morning, good afternoon, good evening), and only later acquired an association with telling someone the time, along with its idiomatic sense.
How to pronounce "give the time of day":
To acknowledge someone; to give someone respect or attention; to tip one's hat
Example: "If you're lucky, she might give you the time of day."
To not acknowledge someone; to snub someone; to disrespect someone; to ignore someone
Example: "He won't give the time of day to someone like you or me."
Example: "I tried to say "hi", but she wouldn't give me the time of day."
To tell someone the time of day by looking at one's wristwatch, etc.