Your phone almost certainly has a SIM card located in a slot on the side or top of the device. It's under a tiny hatch that you open with a special tool that came with your phone, or once you've lost that tool, it's opened using a paper clip.
The SIM itself looks a lot like the memory cards in your digital camera. That should be no surprise because that's what it is—a memory card.
Phones on GSM networks, meaning T-Mobile and AT&T in the United States as well as nearly everyone else outside the United States, have had these cards since the beginning of mobile phones. With the advent of Long-Term Evolution (LTE) technology, they're in virtually all phones.
SIM cards contain the basic information about your phone, including the phone number and your carrier. The memory on the card also allows you to store additional information, such as the phone numbers of your contacts.
Those cards are about to disappear if talks between Apple, Samsung and the GSMA (the international standards organization for mobile telephony) are fruitful. Right now, according to a story in the Financial Times, the groups that have to deal with the cards are ready to ditch them. This includes the mobile carriers who use them including AT&T and Deutsche Telekom, majority owner of T-Mobile.
Phone makers don't like SIM cards because they take up increasingly valuable space inside handsets and they require failure-prone parts, such as the trays that hold the cards inside the phones. The cards and the provisions for the cards also cost money, and nobody likes that.
Carriers don't like the cards because they are a logistical nightmare. They have a separate supply chain from the phones themselves; they have to be accounted for like money; and they're a source of failure, which means calls to tech support and a procedure and service infrastructure that also costs money and can create problems for customers.
Customers used to like SIM cards a lot because it allowed people to have more than one phone that they could use while keeping the same number. But with the growth of smartphones and their role as fashion accessory, that's changing.
Adding to the complexity for customers, there are now three different sizes of SIM cards, and they're not interchangeable. While you can buy an adapter that lets you use a smaller SIM in a phone that holds a larger one, few people seem to take advantage of those.
The replacement for traditional SIM cards is what's called an e-SIM, which is basically the circuitry of a SIM card embedded inside the phone. The e-SIM can be remotely provisioned so that a customer can change carriers or phone numbers as needed. Gone would be the ability to move your card among several phones.