Google Home users can now set one-off and recurring reminders (daily or weekly) and even set reminders for months down the road. Google Assistant also understands context - if you ask it to remind you to walk the dog at 6 while you get ready for bed, for example, it will know to set the reminder to 6 AM. Reminders you set on Google Home will also notify your Android phone, as long as it's running Android M+. In addition, if you have more than one user on Google Home, you'll only hear reminders for you.
Sure, Alexa has had this feature since June, and Apple's Siri has done the same thing for years (though only on your iPhone), but it's good for those who opted for Home instead of one of Google's competitors. You can check out all the details on Google's Home support page, including how to check and update your Android version on your phone, set up multiple Home users, setting and managing reminders and how to deal with reminder notifications on Home or your handset.