Your home can automatically switch between Home and Away modes when you set up either Home/Away Assist or Home & Away Routines with presence sensing. When you leave and come back, your home will switch modes, adjusting the behavior of your products. But you can also manually put your home into Home or Away mode.
You shouldn't need to manually switch between Home and Away modes since presence sensing will automatically do it for you. But manually switching to Away mode can switch your home faster than waiting for Nest to notice that you've left. Manually switching can also be helpful for troubleshooting if your Nest products didn't switch as expected. For instance, you can manually set Home mode so you can stay warm while you troubleshoot a thermostat issue.
Note: If you are at home and manually put your home into Away mode, it will remain in Home mode for about 5 minutes. This is to give you some time to leave. After 5 minutes, if any of your Nest products notice you're at home, they'll automatically switch back to Home mode.