Because it's the only connection to the club, the grip is one of the most important components in golf and thusly, one of the most difficult to change.  There are references to weak, neutral and strong grips throughout the teaching world and of course every instructor has his or her opinion on which is best.

     When you get a chance, stand with your arms hanging in a relaxed manner at your sides; raise both until they are in front of you and parallel to the ground.  If you're like most people, your palms will face one another.  Now, if you bring them together and fashion a golf grip, you'll notice that the V's formed by the thumbs and index fingers tend to point at the respective ears.  This is a neutral grip; or because it's formed by your hands in a natural position, a natural grip.

     So, any time your hands pass in front of you, they tend to return to this natural position.  And if the swing begins with the clubface square to the target, the clubface tends to be square at impact and produce a fairly straight shot.

     Notice the use of the word "tend"?  The ability to return the clubface to square at impact depends on much more than just a compatible or neutral grip.  Balance and reflexes play a huge roll.

  A final thought:  I prefer to see the V's mentioned above pointing to areas as opposed to specific parts of the body, giving each player the room to adjust for differences in physique and flexibility.  The range for the V of the leading hand is between the chin and trailing ear.  The range for the V of the trailing hand is between the trailing ear and shoulder.  When the V's leave these ranges, adjustments and compensations have to be made during the back and forward swings to gain a square clubface at impact.
Once again, there are slight variations from one touring professional to the next, but you won't see them stray too far from this position.  When you do, you'll also notice them straying from the top of the money list.
"The less skilled the player, the more likely he is to share his ideas about the golf swing."
"Every time a golfer makes a birdie, he must subsequently make two triple bogeys to restore the fundamental equilibrium of the universe."
"If it ain't broke, try changing your grip."
"A golf match is a test of your skill against your opponent's luck."
"Golfers who claim they don't cheat also lie."
"If you're afraid a full shot might actually reach the green while the foursome ahead is till putting out, you have two options:  you can immediately shank a lay-up or you can wait until the green clears and top a ball halfway there."