In general, in chess if the opponent can't pressure, attack, or disrupt it, then it's strong. In terms of a center this could be any number of different board configurations.
Id' say the quintessential "strong center" is two pawns abreast in the center when the opponent can't attack them or force them to move.
The reason a "strong center" is useful, IMO, is more important than what does and doesn't constitute a "strong center." It's useful because it will intrinsically give your pieces more mobility and the opponent's less. Generally this is because you'll have 3 to 4 ranks of squares to make use of vs the opponent's 2 to 3. Also when you can't make use of the center your flanks are somewhat disconnected. For example the player with the strong center may quickly shift his pieces for a kingside attack while the opponent will be slow to bring defenders.
Hi, can someone please explain what a strong center is?