Using the "s" will show possession of an object. Example, I drank from Tom's coffee cup. I think "Of" is a preposition that normally shows a location of an object, but can also show an amount. Example, I drank a cup of coffee. In this case "cup" is the amount of "coffee" I drank. However, English speakers will often replace "have" with "of" incorrectly. Good example: I should have gone with her. Incorrect example: I should of gone with her. This happens because in English we can combine "should have" into "should've" which sounds a lot like "should of".

The answer might not be simple to answer completely, but here are some ideas: When you're speaking about something belonging to a person you'll use that person's name with an apostrophe + S suffix. Robert's car. Jane's beautiful voice. If you don't use the person's name you should use the possessive pronoun, as in His car. Her beautiful voice. When speaking of a person, we don't say "of [Person's Name]". We don't say, for example "the little pony of Sean". Instead, we say "Sean's little pony." However, there is a different way of expressing ownership by a person, less commonly used, where you can say "that little pony of Sean's". When you are writing you never need to worry about that version, but it can be used if you want to specify something especially good or especially bad, or something else you are highlighting about the pony. For example "That little pony of Sean's is very fast," or "That car of John's is very nice looking.". I'd be interested in hearing which text was corrected to use "of [X]" instead of using the apostrophe + S.