Autopause (introduced in 1.0.4) is an option in the Settings menu that will pause the game while talking to an NPC or opening your inventory in single player mode. This includes all situations that would open your inventory automatically, such as looting chests and piggy banks.
The main advantage to autopause is that 'non combat' functions such as shopping, inventory manipulation, and looting become much safer. In some ways, combat becomes easier as well, since the appropriate healing items can be easily swapped in and out of hotkey slots without more damage being taken. Because the action is paused, and the Save and Quit option is available on the inventory screen, autopausing in a near-death situation provides a form of instant escape. You can also queue up throwing multiple items at the same time in this paused state.
The most irritating side effect of autopause is the inability to hot-click while in the inventory screen. This makes chest management in your home more difficult, as you have to deal with the contents of the first chest, close your inventory, open the next chest, close your inventory, etc. Crafting and sorting your loot after an adventure becomes much more tedious.
When in autopause mode, lava continues to bubble. When unpaused, all of the bubbles pop and dissipate.
Stats for items equipped don't update while autopaused. For example, if you start at 5 defense before you open your inventory, and put on better equipment, you won't be able to see your updated total defense until you exit and re-enter your inventory. The same applies to set bonuses.