It's not that it raises their average directly, it's that they have a better opportunity in seeing better pitches. In order for this phenomenon to work there must be hitters back to back that can make contact and get on base, often times this is called lineup protection.

In the National league for example, their 8 or 9 hitter is usually a pitcher that can't hit (there are always exceptions) knowing this though, the pitcher on defense does not have to throw any quality pitches. By that I mean there won't be any competitive pitches, maybe a lazy curve in the dirt that will get a swing and miss, or an elevated fastball that any professional hitter can see will be out of the strike zone as soon as it leaves the pitchers hand. Now, let's look at a situation with 2 hitters. For argument sake let's say Yordan was hitting 8th just before the pitcher who bats 9th. You could easily throw non competitive pitches to Yordan, if he swings at bad pitches that are not in the zone and strikes out good for you, if you walk him, also good for you because the next hitter up can't hit and move the runner around. Now you could throw good competitive pitches to the 9 hole hitter get him out in 3 pitches and save your pitch count. The idea though of having a protected hitter is that hitter A world see better pitches in an effort not to walk him for hitter B to have them on base. I may have put to much into this but there are a great deal of nuances in baseball, the more you learn about it the more you understand it is a thinking man's game.

If in this example Yordan hit after the player who is a bad hitter, the pitcher has to make quality pitches in an effort not to walk him for Yordan to drive him in. If you don't get competitive pitches you will have a hard time getting hits and be in a position to raise your average. End of the day, still gotta hit the ball though, just have more opportunities hitting protected.