To be clear, that certainly doesn't mean you need to stop using the phone. There's no Google magic at play here that will disable your device or otherwise hinder its functionality (aside from the usual wear-and-tear that comes with operating an aging smartphone).
However, if you do choose to hold off on upgrading, you won't have access to any of the latest Pixel-specific features, major upcoming versions of Android, or security patches. Android 10 is the last big software update you can expect to receive.
For those who haven't been keeping track, the Pixel 1's official support period lasted around three years -- that's certainly not awful, and smartphones from other phonemakers often stop receiving updates far sooner. However, it's also not ideal, especially given Google's role in the Android eco-system. If anything, you'd think the company would have an easier time supporting its phones over longer periods due to its position as the OS' developer.
Apple, another first-party phonemaker (all of the tech giant's devices run on its own operating systems), typically continues to roll out software, security, and feature updates to its gadgets for roughly five years.
Regardless, there's not much that can be done about it now. If you are a Pixel 1 owner, we certainly hope you're able to keep using the device as long as possible, but for security reasons alone, it might be worth considering an upgrade sometime over the coming months.