There are two types of AMIs/instances: EBS boot and instance-store (sometimes referenced as S3-based). You are probably using EBS boot, so this answer will relate to that type.
An EBS boot AMI is an EBS snapshot of a boot EBS volume with some extra attributes including:
- Registered as an AMI with an AMI id
- AKI (kernel)
- ARI (ramdisk)
- architecture (e.g., 64-bit)
- block device mappings (e.g., where volumes should be created/attached)
- description, name
- permissions (who is allowed to run the AMI)
If you create an AMI of the running instance, you should be able to start new instances in the same state. Make sure you test this process so that you know it works.
If you simply snapshot the EBS volume(s) of your running instance, you will be able to create volumes from those snapshots to access the configuration and data.
It is also possible to take an EBS snapshot of an EBS boot volume and register it as an EBS boot AMI so that you can run more instances starting with that state. When registering the AMI, you'll need to specify the correct AKI, architecture, and other meta-data in order for this to work, so research and practice before you trust this approach.