Count the squares. White’s pawns on d4 and e5 control c5, d6 and f6, so Black’s knight on g8 cannot use f6, his bishop on f8 cannot use d6, and his bishop on c8 is staring at his own pawn on e6. White’s pieces get four ranks to play with. Black’s get two and a half.
8 
7 
2 
a b 
c 
d 
e f h 1 That is space: not territory in any grand sense, just the number of useful squares your pieces can stand on. The side with more of it has an easier game to play, because he can move a rook from a1 to h1 in two moves while his opponent shuffles a knight between b8 and d7 waiting for something to open.
Counting it, roughly
The quick count is how far up the board your pawns sit and which way they point. White’s e5 pawn is the only one across the halfway line, and it points at Black’s king, so White plays on the kingside. Black’s pawns on c5 and d5 point the other way, at b4 and c4, so Black plays on the queenside with …cxd4 and pressure down the c-file.
That is the useful part of the idea. Space is not a score you win with. It is a signpost. Attack where your pawns point.
The cramped side trades
If you are the one with two and a half ranks, every trade is a small victory. Six pieces in a small flat is a nightmare; two pieces in the same flat is fine. So swap a pair of knights, offer a bishop, and keep offering.
The other half of the cure is a pawn break, timed to open a file for the pieces you have left. Black’s …f6 in that structure hits the head of White’s chain on e5, and if the pawns come off there the f-file opens and the knight finally gets f6. That is real counterplay rather than passive shuffling.
The trap in owning space
Every pawn that grabs a square in front leaves a square behind. Push to e5 and d6 stops being defensible by pawns for ever, which is exactly how a space advantage turns into a weak square with an enemy knight sitting on it.
So the rule of thumb has two halves. Take space with pawns while your pieces can support them, then stop pushing and bring the pieces up. If you want to see how the strong side converts it, the opening puzzles are full of positions where the extra rank is what makes the tactic work.