Where Q codes come from
Q codes are three-letter abbreviations, all starting with Q, that began in the early 1900s so that ship and shore operators could exchange common messages in Morse code without sharing a language. The International Telecommunication Union still maintains them. Each code has two meanings: followed by a question mark it asks something, and on its own it answers or states it. QTH? means "what is your location?", and QTH London means "my location is London".
Radio amateurs use a small set of Q codes all the time on CW, and many have slipped into voice and everyday ham slang. A QSO is a contact, a QSL is a confirmation card, QRP means low power, and QRT means closing down.
How amateurs use them on voice
Strictly speaking Q codes are for Morse, but a few are so convenient that they're used on SSB and FM too. You'll hear "the QTH here is Manchester", "QRZ?" after a pile-up, "QSY to 145.500", and "QSB is heavy tonight". Keep it to the common ones. On voice, plain language is clearer for everyone, especially newer operators.
Giving a good signal report
Readability matters more than the S-meter. If you copy every word easily, the R is 5, even if the signal is weak. For S, use what you hear, or your meter if it's calibrated. Most give 5 and 9 by habit in contests, and that's accepted there, but an honest report is more useful in a normal contact.
Questions
What does QTH mean?
Your location. QTH? asks where the other station is, and QTH London means you're in London. Many amateurs give their Maidenhead locator as well.
What does QSL mean?
It means “I acknowledge receipt”. Amateurs also use it for the card or electronic confirmation, such as LoTW or eQSL, that proves a contact took place.
What does 73 mean?
73 isn't a Q code. It's from the old telegraph numeric codes and means “best regards”. 88 means “love and kisses”, and you'll mainly hear it between friends.
What does 599 mean?
It's an RST report: readability 5 (perfect), strength 9 (extremely strong) and tone 9 (perfect). On voice the tone is dropped, so it's just 59.