There's a red and a black side on a table tennis raquet.
Does the color of the side have any significance? E.g. is the black side suppose to be used for the forehand and the red side used for the back hand?
According to the official rules (referenced here):
The surface of the covering material on a side of the blade, or of a side of the blade if it is left uncovered, shall be matt, bright red on one side and black on the other.
The reasons for this rule are described here:
The Two Colour Rule
Since 1 July 1986 the rules of table tennis state that one side of the racket shall be bright red and the other side black.
This rule was introduced because of the increased use of "combination" rackets in the late 70s and early 80s.
Players were using the same colour rubber on each side of their racket - but each side was a different type of rubber - and this made it very difficult for the opponent to know what type of spin was being imparted onto the ball.
So if you're planning on taking part in authorised table tennis events, make sure that you buy the correct colours.
Another article suggests that:
In table tennis the two color rule is used to ensure that the opponent has a fair chance of telling which side of the bat has been used to hit the ball. Before the two color rule was introduced, any color could be used for table tennis rubbers, and players were using combination bats with the same color on both sides and twiddling the bat, making it very difficult to tell which side was hitting the ball.
This was considered to produce table tennis which was not spectator friendly, since it was difficult for uninformed spectators to understand why players were making seemingly simple mistakes.
It seems that the rule was made to make competition more fair - it would give opponents a chance to determine the type of spin that was being imparted and also to make the game more fun to watch.
I couldn't find anything in the official rules, but unofficially it looks like it's for your opponent to be able to tell which side of the bat is used so you know the type of spin put on the ball. Not sure what stops people from flipping it around as they play though...
The color does not have any significance. The thickness of the rubber and whether it has the dimples (called "pips") facing outwards or inward does have some significance though in terms of the surface playing more offensive (imparting more topspin - pips out) or defensive (pips in). The height of the pips plays a role also. See the section titled "Table Tennis rubbers - are they all the same?" on this page.