Understanding iphone sim cards for iphones?

I'm planning on buying an unlocked iphone from a family member. They said something about the sim card from their At&t iphone? Once they remove the card the phone is open for any service. I'm with verison. What i don't understand is the purpose of the card. When i buy the phone will i need to purchase a sim card? And will i have to pay for a data package? For internet and stuff like that?

Once they remove the sim card the phone isn't necessarily open for any service.

First, if it's att its on the GSM cell network, won't work on Sprint or Verizon or any other service on CDMA standard.
Second, they have to legally unlock the phone by fininshing their contract or paying it off and calling att for instructions on unlocking it.
The sim card is what controls your phone, access to a provider and any plan you choose, without a sim, the phone is dead.
You will need to sign up with a provider which uses GSM, Att or tmobile, and select a plan, then you get a sim card and start paying them. You will pay for whatever plan you choose.

Removing a SIM does not make it suddenly able to work on any other service. The phone would need to be unlocked for that to happen.

Its Verizon by the way.

The SIM is basically the phone's identity on the carrier network. Contains the phone number, & access to that network. No SIM, no phone in effect. Yes you will have to pay for a data plan (which is internet btw) since it is a smartphone.

Also there's no special iPhone SIM card. A SIM is a SIM.

An unlocked iPhone is a GSM phone. That means it can be used with AT&T, T-Mobile, Straight Talk and a few other GSM networks. It is used with a sim card from the network that carries the account data and provides service. The phone can't be used on CDMA networks such as Verizon, Sprint and Virgin. Such networks do not use sim cards.

Most networks require both a talk plan and a data plan with an iPhone. However, since you are providing the phone, you should be able to avoid signing a contract and just get month to month service.