Don't move a piece twice before move 10

I am a beginner and I've heard this recommendation more than once, yet I see Grand Masters moving their white bishop 3 times routinely within 10 moves. Can anyone explain?

Depends on the opening

White should probably move his bishop here again.... but chessbase does have 4.0-0! occur in a few games

All of the recommendations and opening principles you hear are just guidelines, not hard and fast rules. The key is to follow them until you learn enough to understand the exceptions. And as demonstrated above, the main exception to this one would be if your piece is attacked and you need to move it to save it.

And it has nothing to do with move 10. The guideline is don't move the same piece twice in the opening. When does "the opening" end? When all your pieces are developed!

Now go read Irving Chernev's "Logical Chess: Move by Move". If you're asking a question like this, then that's the best book for you.

This separates grandmasters from the vast majority of us.

Depends on the opening in some a knight may need to move three times to get to a move active square.

It is said because generally in the opening, the goal is to develop all the pieces to active squares so they can take part in the game. When beginners usually play the same piece twice, they are wasting time and allowing the opponent to get faster development, which is the main reason why this is discouraged. However there are exceptions, obviously when moving the same piece allows you to win something or gain an advantage, or in openings which have you purposely move a piece multiple times, which grandmasters sometimes do play. This is an exception to the usual recommendation of not moving the same piece, because openings are usually well studied and tested by master players, so it is all planned out, not moving the same piece aimlessly like lower level players. 

This is why I call these concepts "principles" and not "rules." Rules sounds too rigid. These principles are USUALLY right, but there are some exceptions. GMs tend to know when to correctly deviate from the normal.

Implementing a chess principle blindly (typically as a beginner) is better than not knowing it at all, but ideally you should strive to try and understand WHY the principle works the way it does. 

In this case, moving the same piece twice early on is generally not recommended because the tempo (time to move) can usually be better spent on developing another piece. What is often times better? Having two pieces developed (one move out each) or having one piece developed and then relocated again? Having two pieces developed is almost always better!

There are exceptions (as some openings highlight), but typically the instances where a piece moves multiple times early on are positions somewhat closed in nature, so development (and especially tempi) isn't as urgent as in open positions. Moving the same piece might also be the logical way to avoid capture, so sometimes it is more or less forced. 

Thanks to all. I started reading "50 Essential Chess Lessons" by Giddens and the game is starting make sense.

This is a good basic rule, but sometimes it needs to be broken.

The principle "Don't let your opponent take your pieces for free!" Takes priority over the principle about moving your pieces twice

i think this is a pretty good opening

Actually, I disagree! Playable? Sure. "Good?" I don't think so. I consider this opening dubious because I believe that Black can close to refute it (if not outright) if they don't mind playing sharp in the Polerio Defense.

4. Ng5?! is inferior to development moves or contesting the center. 4. O-O, 4. d3 and 4. d4 (as well as some others) are stronger moves I think.

While I wholeheartedly agree, it should be pointed out that most beginners start step two WAY too early. 

One of Dan Heisman's guidelines for beginners is "Don't have a better idea." In other words, stick to the guidelines, even if you think you have a reason not to, until you've truly gotten a good feel for why the guidelines are recommended so much.

@Cicero3993 it's not necessarily about developing your pieces as quickly as possible, but rather not allowing your opponent an advantage in development. If your opponent makes a non developing move such as moving a pawn or the same piece twice, and you do the same, and there is no meaningful difference in development, then neither side has an advantage. Another reason for moving a piece twice is to get it to a stable square where it cant be easily driven away. It's a useful rule that applies at all levels. Many victories have their origins in a development advantage gained in the opening due to an opponent wasting time.

That's because developing quickly and castling the king quickly wins the vast majority of the games. Obviously if you see a fork and the knight has to move two or three times after development, you may want to do it. The same goes for pawn pushes and adjusting pieces because there is an opening where there is a better placement. 

Just to add, and getting more technical, a development advantage is temporary, an opponent can catch up, so the way to cash in a development advantage is to convert it to some other advantage, normally a material advantage, via a combination or tactic that wins a pawn or piece. A material advantage is more enduring. This is the idea behind a Gambit. Generally the player that is ahead in development should try to open up the position by trading off pawns, to open lines for their pieces to attack. The player behind in development should aim to keep the position closed by pushing pawns, until they have caught up. Rules of thumb.