Originally Posted by Boz
For quick and dirty, think of advantage as +5.
Please don't. It's much more nuanced than that. If you need to think of advantage as a flat bonus, +3 is much closer to the average value.

A more accurate way to think of advantage is that it is more useful when you need a middle value to succeed and less useful when you need an extreme value to succeed. For example, rolling against a DC 20 with a +0 modifier - with advantage, you've got a 9.75% chance to roll your 20 and succeed. A simple +1 bonus gives you a 10% chance since you succeed on either a 19 or 20.

For combat modifiers, advantage is often more powerful than modifiers due to 5e's bounded accuracy - you usually need a value in the middle to succeed. For skill checks, especially hard ones, you'll often be better off with a modifier.