An IP address is a numerical representation of where a device is connected to the internet. It’s how you identify where something is and, to some degree, what that thing is.
Your online IP address is offered by your browser to every single website that you visit. Typically, websites either throw out this information, use it to block denial-of-service attacks, or save it for analytics to help refine content or targeting.
For the majority of sites that you visit, it's not used in any way that personally identifies you.
But here's the thing about IP addresses…
Even though the vast majority of sites do not use this information to identify you, if your IP address stays the same for many months or years at a time, it becomes searchable after the fact! Many sites innocently expose their own visitor logs to the internet — or someone posts an email with all of the headers still included. For this reason, if you search for your own IP address (one that you've had for a few years), you will see remnants from your past floating around the internet … little personal details that you might not wish to be so highly correlated with your identity.
To address this problem, privacy-concerned or paranoid individuals will periodically force their router to acquire a new IP address from their internet service provider. This is not difficult to do. Login to your router as admin, and look for a feature called “release” and “renew”.
When you complete this process, verify your new IP address with an outside search just Google “My IP address”). If this does not change your IP address, it is because your ISP sees that it is coming from the same drop point, and they are choosing to preserve continuity. In that case, turn off the router before you go to sleep. When you wake up, it will pull a new IP address.