Meaning in the lecture
Zhang describes natural acceptance as acknowledging and accepting what has happened and the accompanying experience, while doing what one can. This passage summarizes it as accepting distress and taking constructive action.
The idea includes both an attitude toward experience and a requirement to act. Retaining only one part can distort its meaning.
How it differs from giving up
The speaker explicitly retains the idea of making one's best effort and working toward the best possible outcome. Natural acceptance should therefore not be read as avoiding problems, abandoning work or study, or ignoring real harm.
Related concepts
Cognition, emotion and action explains the distinctions used in the lecture. The 24-character principles develop different aspects of acceptance and action. Read these formulations in their original context.