Is it wise to buy a refurbished iPhone?

Refurbished iPhone 5s from Hong Kong, is it worth buying?

I'm a frugal type of person, I want to own an iPhone for a change (since I've been using Android). IPhones can be expensive but refurbished are cheaper. I also preferred 5S since it looks nice for me, and the 6 doesn't have refurbished yet.

Is it worth buying? What are refurbished to be exactly?

Firstly, to answer your question, for any electronics, it depends on what part is refurbished. If it is a cosmetic part like the case is replaced due to scratches or a replaced cracked screen, should be fine as long as the screen is still touch screen (where applicable) But if it is the electronic part you should be careful in case the parts aren't done properly. Always test the refurbished product on site/in store and never buy over the internet (for a refurbished item) unless you really trust them or they GUARANTEE a refund if faulty eg Seconds World, stuff like that. Check if it still has VALID warranty. Invalidated but unexpired warranty is NOT usable warranty! (It can be voided if refurbished by an 'unauthorised' person ie other than apple themselves.)
Secondly, I JUST finished a question on iphones when I saw your answer and came here. I always only had Nokias. I have always hated Mac, Apple and iphones. Then someone gave me an IPHONE for christmas. I thought maybe I should try using it before saying I hate it, but no, it just justified why I still hate it for the same reasons as before, and now more reasons. I would try to convince EVERYONE who want an iphone to not get one. Seriously. They are all hype. Everything you get in apple phones you can get in another smart phone, without the hassle. The lack of customizability is just the beginning. If you really want to, you'd have to have it jailbroken. That would void the warranty. Then there's problems with getting the technical side to work. Search online for 'iphone does not alert new messages when locked' and you will see. Also unlike some other android phones, iphone even the latest one which I have, does not do split screen. When you call, the other person's voice is basically in audible, and unless you put the call on loudspeaker you can't hear them. They can't hear you either, (I'm a loud speaker, I speak loudly) I have had multiple people say they can't hear me when I'm talking on the iphone. Even my Nokia 6300's sound is Way better even on the lowest setting. For them to hear you, you need to literally, (I just had a call 10 minutes ago) put the end of the phone with the microphone right up, short of putting it IN your mouth, to talk. I used to wonder why people with iphones talk by putting the call on loudspeaker and bringing the bottom corner up to their lips when calling, I used to think that is annoying, I don't want to hear your call. Now I know why! Err, They lost the receipt so I can't go get a refund or exchange. I'd say stay with your andriod or see if you have a friend with an iphone who is willing to swap phones with you (Oh! Did I mention apple always has to be 'different' in an annoying way ('ipods AND mp3 players.'ipods ARE mp3 players!), they use a different sim card and need a special tool to open the special secret compartment for the tiny sim that if you take it out and cough and shake your hands by accident you lose the sim) AND the sims are compatible, then you could use their iphone for a week and they use your android for a week. Don't forget to take out your personal files (which by the way is not as easy in iphones).

Refurbished phones are ones that were bought, returned, looked over (fixed if need be) & put back up for sale.

They should be fine in most cases & if not should be able to return it to get a proper working one.