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[CriminologyProf]

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[OmegaStarScream]

An encrypted private key helps against those who see the private keys and not against those who created the unencrypted (third party service) private keys. In other words , you won't be able to protect yourself from whoever generated that address and private key for you.
I suggest making an address from Bitaddress.org -> Paper wallet -> Encrypt it using a passphrase and then print it so It feels like a credit card (not sure how to do that) , Its possible to give the encrypted private keys and your address to a third party to print them for you but letting them generate the address for you like you did is not secure.

[altcoinhosting]

OmegaStarScream is correct, i only wanted to put it into very simple wording...
You could look at your private key as a code to a safe (the example is not completely analog, but it's similar).

You have a safe, an this safe can be opened by code 12345. This is the code to open the safe, the only code.
If you would save this code online (or write it on a piece of paper), everybody who gets their hands on the code can get into your safe, so, it might be wise to encrypte the code. So when you print it out while it's encrypted, nobody can use it straight away.
You write your own (very basic) encryption algorithm.. 1 = a, 2 = b, 3 = c,... So your encrypted code is "abcde".
Offcourse, when you go to your safe, you cannot type in "abcde". You have to decrypt your code before you can use it to open your safe. So, when you get to your safe, you have to to convert your encrypted code "abcde" back to "12345" before it can be used to access your funds.

Same thing goes for your private key... you can encrypt it, so you can safely print it out, so that when it get compromised, the person finding the key cannot use it directly, but it's still the same private key, it needs to be decrypted before it can be used. (offcourse, the encryption used to encrypt a private key is much stronger than the imaginary example i gave)

[altcoinhosting2]

But this brings up another question:

All of the paper wallets I've seen or used contain QR codes for each key, as well as a string of numbers beneath these keys. If these are the keys, then what is the point of encrypting something that is already in plain view on the wallet itself?

Well, you can generate a QR code from the encrypted private key to

Usually, an encrypted paper wallet contains both the encrypted private key and the address both in textual format as a qr code, so you cannot use the private key without either knowing or brute forcing the password.

[hdtqisg]

I think you must to know how people encryption priv key. Without it. there is no way to use it

[hdtqisg]

more info can see here
https://www.bitaddress.org/bitaddress.org-v3.3.0-SHA256-dec17c07685e1870960903d8f58090475b25af946fe95a734f88408cef4aa194.html

[LoyceV]

I may have a masters degree but it definitely isn't in computer science, so this sort of thing is very difficult to grasp for me if explanations are in technical terms.

In this case it is important to understand a few fundamentals before using Bitcoin. Most important for now: if you use a paper wallet, you have to swipe the entire balance. If you only use a part, the remainder does not "stay on the paper wallet" but is transfered as change to another address. Make sure not to lose the change.
To make the transfer, you'll need a wallet.

I was thinking of a pass phrase being like a PIN number for a debit card, an extra security needed to access an account. I didn't realize it was just a way to decode an account number.

Don't think of it as an account, think of it as a wallet. But with one crucial difference: the moment someone has seen it, he can always use it.

All of the paper wallets I've seen or used contain QR codes for each key, as well as a string of numbers beneath these keys. If these are the keys, then what is the point of encrypting something that is already in plain view on the wallet itself?

I suggest you just try it! Make a few paper wallets. Some encrypted, some not encrypted. Just see/feel/test the difference.

bitaddress.org has already been mentioned as site to create a (nice looking) paper wallet. Another option is bitcoinpaperwallet.com.