ISPs normally assign a single public IP address to each home Internet connection. With IPv4, there are simply too few addresses for every device to have a public address of its own.
Your router has a feature called Network Address Translation (NAT), or more accurately Network and Port Address Translation (referred to as NAT and PAT). When you make an outgoing connection to a website, the NAT function changes your computer's local private IP address into the router's public address on the Internet (or in some case such as in an apartment block, to an address on another subnet covering the different apartments). The router remembers which addresses (source and destination) and which ports (source and destination) were used by the computer and by the router when the connection goes out on the Internet. When a response comes back, the router checks the addresses and ports (although source and destination are swapped over) and does the reverse mapping.
If a computer on private address 192.168.0.11 with source port 12345 opens a connection to an http site on address 123.123.123.123 port 80 (the http port), the router will change the 192.168.0.11 to its public address (say 111.222.112.221). The destination address and port are unchanged. The source port may not be changed; however, if another computer on the private network (192.168.0.12) opens an http connection to the same website, and by chance is using the same source port number, then there is nothing to tell the site that it is a different connection. In this case, PAT comes into play and the router changes the source port number to one it is not using on the Internet. When the response comes back reverse NAT and PAT can route the response to the correct computer.
Although the destination port on an outgoing connection is normally predefined (80 for HTTP, 443 for HTTPS, 25 for SMTP, etc) the source port is picked at random by the source computer's operating system from the higher numbered ports. Open two connections from two tabs in a browser with both connecting to the same site, and the connections will have different source port numbers assign by the operating system. This will happen even without a NAT/PAT router being present
The NAT function in the router is why all computers on a home network can have the same public IP address.
Depending on how your ISP assigns and manages public addresses, your public address may never change. It may change spontaneously normally only at a maximum of perhaps twice a day unless you disconnect from the ISP. Disconnecting from the ISP for a period of time can mean the ISP will assign that address to someone else and you will be assigned a different address when you reconnect.
Generally there is no need to change your public IP address. If your router is working correctly, it will only let in packets from the Internet that are responses to outgoing packets. If you want to run some form of Internet accessible server, then you will have to configure port forwarding that will tell the router to allow packets arriving on the public IP address with a specific port number, such as 80 for an HTTP web server, to send these packets to the specific computer on your internal network that is hosting the HTTP server application.
I hope this helps.