What does No contract mean (iphone5s)?

Okay so I'm saving up to buy the iphone5s, I have verizon. I was told that getting it with no contract would be better. But my friends said that having no contract means I can't have; internet, unlimited texting or calls, and that basically it would be as good as an ipod. They also said that you have to have a contract. This doesn't make sense though cause why would the no contract be more expensive, if it meant that you can't get all the features I mean it is an iphone so isn't that the point? I know that for a 2 year contract you pay monthly or something and I can't do that (16 with no job). So my questions are:

What does it mean to have "no contract" for an iphone5s?

Is it better/ worth it to have no contract?

Can I still have unlimited texting/calls, internet with no contract?

and ya if someone can just clarify it would be very much appreciated thanks and sorry if it was confusing.

There are two ways you can purchase the iphone. You can either pay full retail for it (which is $649+, depending on which storage space configuration you get), or you can sign up for a 2 year contract, which will subsidize the cost of the phone. In this case, it would cost $199+. However, with the service contract, you will need to pay for service each month. You can terminate the contract before the 2 years are up, but then you will have to pay a fee (that will essentially be paying off the rest of the phone).

In other words, buying it without the contract, is more expensive up front, but will potentially allow you to get a cheaper service plan (I'm not sure if Verizon lets you get a prepaid plan on iPhones) or use it without phone service altogether, whereas the contract plan is cheaper up front but will require you to pay a contracted amount for service each month.

In either case, the phone has the same capabilities; the texting/calling/internet depends on whatever service you sign up for.