Moving your bishop like that is called a [fianchetto](http://en.wikipedia.org/wiki/Fianchetto).  There are a lot of openings which fianchetto the king's bishop; what you are describing sounds somewhat like the [King's Indian](http://en.wikipedia.org/wiki/King%27s_Indian_Attack) for white.

The advantage of fianchetto-ing your bishop is that it very quickly puts the bishop on the long diagonal, its most powerful position.  However, it takes two moves, and weakens your kingside (specifically the `f3` and `h3` squares), giving your opponent potential areas to attack.  For example, a common plan for black in many openings (if his pawn structure allows it) is to force the trade of bishops by `Bd7`, `Qc8`, and `Bh3`.  Once the bishops are traded, your king would be very vulnerable to attack.

Traditionally (beginning with [Steinitz](http://en.wikipedia.org/wiki/Wilhelm_Steinitz)), it was taught that one of the goals of the opening phase was to control the center by occupying it with pawns.  However, [Nimzovich](http://en.wikipedia.org/wiki/Nimzovich) introduced [hypermodernism](http://en.wikipedia.org/wiki/Hypermodernism_%28chess%29), which states that the center should be controlled from a distance by pieces, not occupied by pawns.  Neither view is more correct than the other - even today, both have very strong Grandmaster supporters, and accepted opening theory draws from both sides.  I mention this because yours is a hypermodern opening.