Single primes are used to mark feet, and double primes for inches. They are no substitute for apostrophes and quotation marks—a mistake made even in (shudder) company logos.
The apostrophe, or single closed quote, is used for contractions or possessives. It’s also used as an elision (e.g., “the ’30s and ’40s were horrible decades for Europe”—the apostrophe stands in for the missing “19”). Some refer to typographers’ quotes as “curly quotes” or “smart quotes.”