The To-Dos feature in Core refers to tasks that can be assigned to employees (or vendors), and given the context of project, client, employee or vendor. Some to-dos do not need any context, but are still recorded as assignments. To-dos can also have a reminder set on them and are easily convertible to time entries. You can create To-Dos from the main menu > Productivity Tools > To-Dos. Check Core Help Center for details.
You can set reminders from your company menu > User Preferences > Notification and Reminders. On the Reminder Settings tab, there are various categories of reminders that you can choose to be informed about. Check Core Help Center for details.