You have two storage options with instances. EBS and Instance storage:
EBS is somewhat like an SAN volume. It exists outside of the instance and is accessed via dedicated ethernet (This is shared between instances based on IO priority). Volumes are billed based on the provisioned size. It does have some benefits over instance storage in that it can be easily snapshotted and moved from instance to instance. EBS limits are practical ones, while you can attach quite a few volumes (up to 1TB each) the available bandwidth will likely be saturated before you can take advantage of all of them.
Instance storage is a disk attached directly to the host hardware. Its included in the instance cost. But it should not be treated as persistent. You will loose any data stored on this volume if your instance is stopped or fails for any reason. This is because at each boot, your instance is assigned to available host in a pool instead of being locked to a specific host.
You can use both types of storage on any instance (Except micro, no instance storage available). Instance storage options however need to be set at launch and can't be changed later. EBS volumes can be added/removed at any time. In most cases, instance storage is disabled by default and needs to be explicitly enabled. Helps avoid the situation of "Why did all my data get deleted?"