[Black Baron]

You can read the "in short" bit and skip the explanation if you like.

An extremely popular and useful thing is to play bishop g4 (for the white it will be bishop g5), thus creating a tie between knight and a queen, should knight go away, the queen will be lost. Should queen go away bishop will eat the knight, and you will end with unprotected king (if you castled there) and double pawns. More often than not it is a sure pass to loosing for the white.
In order to prevent it, either play: 1) pawn h3 (in some openings a liability. The black can sacrifice the bishop for 2 pawns after- queen c8, or d7 or e6, bishop eats h3, g2 eats h3, queen eats h3-->white is in trouble).
2) bishop e2 (in some openings a liability) and move the knight away, exchange the bishops and gg.
3)knight from the queens side to d2, move the queen, them move the tied knight at f3 to some other location.the plan sometimes is problematic.

Apart from the strategical reasons (the tie, or the opening requests )listed above i do not see any strategical reasons of playing h3. I showed you 2 substitutions if you do not want to play h3, in case yo have the tie. If the enemy is threatening to place another piece at g4, playing h3 needs to be considered.
Tactical reasons of course (winning material or f.e gaining a strong attack at the enemy king with king h1 and rook g1 afterwards) are different per game.


In short: Study openings. Without them it will be case per case desicions. read the explanations for general lines.