While you are not logged in, your character will, by default, accumulate waypoint time. However, you can also set your character to grow onions, carrots, barley, or harvest wood or grass.
Under the Main/Utility menu, you will find an option entitled 'Offline Chores'. This will bring up a pop-up box that will allow you to choose which chores you want to do while offline. You can choose any number of chores, one of which is to accumulate waypoint time. For all the chores except waypoint time, you must first manually grow or harvest a certain amount before you can activate that chore.
The results from offline chores are stored in your inventory, so if you are going to be offline for a while, make sure you have a place to stash the results when you log back on.
If you choose only one chore, the accumulation rates are as follows:
If you choose multiple chores, the offline time is split evenly between them. That is, if you choose waypoint time and onions, and are logged off for four hours, two hours will be spent growing onions, and two hours will accumulate into waypoint time.
Be sure to consider the value of waypoint time versus time spent on other offline chores. It is more efficient long-term to build several greenhouses to cover your grass needs, and Ritual of Plant Growth can be used to boost your barley and onion harvests. Barley also gains +10 harvest bonuses each from having the Green Thumb skill and attaining the rank of Journeyman of Worship (those two bonuses come into play when you harvest the barley, so you could grow it, and have someone who has them harvest for you).