Space equals options. The fewer options you give your opponent, the less in their arsenal they'll be able to use as you employ your game.
Multiple points of contact are encouraged to help you stay connected and manipulate your opponent. Breaking their posture, whether in bottom or top position, is vital as head and hips determine how someone can move.
Think of the ground, your limbs, chest, head and hips as points of contact. Each contact point is used as wedges secure or set up a position. Sometimes you can use space as a reactionary tool. Force someone to move into the 'free space' you've intentionally left, then spring the trap.
Space is the difference between hitting a transition perfectly to missing it. It's the failure to secure get tight enough in a RNC. Space is the enemy...
Example: You are passing someone’s half guard but don’t block their hips. That free space gives them the opportunity to re-guard, off-balance and sweep you or find a sub. These options can be limited or completely shut down by controlling the space and keeping the correct points of contact.