Let's think about this for a second
A Security Group is a virtual firewall for an EC2 instance — it defines inbound rules (which ports/IPs are allowed in) and outbound rules (what the instance is allowed to reach). By default, all outbound traffic is allowed and all inbound traffic is blocked — you open up ports like SSH (22), HTTP (80), and HTTPS (443) only as needed (least privilege). An Elastic IP is a fixed public IP address you can attach to an EC2 instance — normally restarting an instance can change its public IP, but with an Elastic IP attached, the IP stays the same.
Let's connect this to a real scenario
If you open HTTP (80)/HTTPS (443) to 'anywhere' on a web server EC2 instance, but only open SSH (22) from your office IP — the public can browse your website, but attackers will have a hard time getting in via SSH. If you stop/start an instance repeatedly without an Elastic IP attached, its public IP can change — so if you've pointed a DNS record (Route 53) at it, you'll want an Elastic IP attached.
Let's look at it together
# Allow HTTP/HTTPS from anywhere, SSH only from your IP
aws ec2 authorize-security-group-ingress \
--group-id sg-0123456789abcdef0 \
--protocol tcp --port 80 --cidr 0.0.0.0/0
aws ec2 authorize-security-group-ingress \
--group-id sg-0123456789abcdef0 \
--protocol tcp --port 22 --cidr 203.0.113.10/32
# Allocate and associate an Elastic IP
aws ec2 allocate-address
aws ec2 associate-address --instance-id i-0123456789abcdef0 --allocation-id eipalloc-0123456789abcdef0$ aws ec2 describe-security-groups --group-ids sg-0123456789abcdef0
# Shows inbound rules: 80/tcp from 0.0.0.0/0, 22/tcp from 203.0.113.10/325-minute try-it
On the EC2 instance from the Basic chapter, open HTTP (80) in its Security Group, then allocate and associate an Elastic IP — stop/start the instance a couple of times and confirm the public IP doesn't change.
A quick word of caution
An Elastic IP not associated with an instance (idle) incurs a cost (while it's associated to a running EC2 instance, it's free) — keep the Free Tier limits in mind.