Base is your ability to stay balanced and grounded when someone tries to move you. A wide, low base with good weight distribution is hard to sweep or throw; a narrow, upright base with bad weight distribution is easy to move.
In the guard, the top player needs base to resist sweep attempts: if your weight is too far forward, a scissor sweep dumps you; too far back, a flower sweep works. Learning to feel when your base is compromised — and to widen your stance or shift weight quickly — is a core self-defence and anti-sweep skill.
Base and posture are related but distinct. Posture is about your spine angle; base is about your foot placement and weight distribution. You can have good posture but poor base, and vice versa.