The idea of mobility and space is directly related to the opening phase of the game and also tied to development. In a typical game both sides fight to control the center and gain space in which to deploy and maneuver pieces in. The French Defense for Black is one such opening where White is allowed a spacial advantage by the line 1. e4 e6 2. d4 d5 3. e5 which leads to the Advanced variation of the French Defense seen below.
As you can see here White’s e6 pawn controls the d7 and f7 squares which the Knight or Bishop could use in the future and additionally the Bishop on c8 is blocked in by the pawn chain on e6. In a position like this if Black isn’t aware of the plan needed his position could become overwhelmed and cramped by the loss a couple of squares and Bishop mobility. There are benefits to a closed structure that you find in an opening like this, the game becomes more positional and the tempo slows down which works well against a tactical and attacking opponent.
Above a continuation from the previous image with what could be normal development for Black has actually lead to quite a good position for white. The Knight being placed on c6 is incorrect as it blocks the pawn from advancing to c5 and breaking the pawn structure which is a typical idea in the French Defense. Pawn to …f6 was played after which attacks the forward point of Whites pawns however f4 can recapture and White is left with a strong center and open diagonals along the c1-h6 and f1-b5 for the Bishops.
In this position you can see that Black is no longer as cramped as in the other opening, the Knight has a purpose in the center, the Bishop defends the c5 pawn, and the Queen eyes the b2 pawn if White moves the c1 Bishop. The computer rates this as equal currently, White has the space advantage on the King side and Black on the Queen side and both play on their respective sides. The French has a chance to be either a slow and quite game or an exciting one since both sides have chances to attack.
Linked is a French Defense Advanced Variation game where White Mates in 20 moves showing the more aggressive side while playing against the French. White plays a sacrificial line drawing the Black Queen into fire while simultaneously developing an attack.