Why is the last move by white, g3 on the board below, considered a bad move? It was in a game that I played recently and my idea was to protect the bishop in f4 and give the other bishop more space to move. But Fritz said that this was a strategically bad move.
Allowing the exchange ...Nxf4 gxf4 simply weakens your structure considerably. The pawns on f2, f4 and h2 are disjointed and cannot protect each other anymore.
Black can immediately start attacking f4 with a following ...Bh6, for example, and your only way to defend that pawn is by moving your queen into a pin. Due to the tactical danger involved, it may even possibly be better to just leave the pawn to its own at this point. In any case, Black will have an easy game attacking all your weak points.
- Qd2: Also protects the bishop, while also putting out the queen (to a square where it is protected by your knights, so after a looming exchange of central pawns, Black cannot rob your castling rights by Qxd1). Limits your other pieces' mobility a bit, though.
- Bd2/e3: At first glance, this loses a tempo. However, on the upside it avoids the exchange on f4 completely, which means that Black cannot get rid of his bad Nh5 (for your comparatively good bishop and thus, as Ian Bush mentions, the bishop pair). The knight is bad because has no squares to move to except g7 (where it would temporarily stand in the way and has to be moved again, losing back that tempo). Be3 overprotects d4 and leaves d2 open for the knights, Bd2 blocks the d-file against queen swaps and gives the bishop mobility on the queenside - both are decent moves.
Other answers have made many good points. But the main reason g3 is a bad move can be reduced to a very simple explanation: The knight on h5 is a very bad piece, it has almost no squares to go to and can easily be threatened to be trapped. The best move in the position is 1.Bd2, this is because compared to other squares for the bishop to move to, it blocks the d-file, preventing a trade of queens after 1...dxe5 2.dxe5.
Here is one sample variation to illustrate how poor the knight on h5 is: 1.Bd2 Bg7 2.Nc3 Nd7. Black has developed logically while attacking the e5 pawn, but... 3.g4 traps the knight and White wins. This means that Black cannot play simple moves and will instead have to spend a few moves re-routing his knight with something like 1...dxe5 2.dxe5 Ng7.
There is a common saying "One bad piece makes a bad position". While not always true, in this case it is.