Action is at the center of the Gita because the book is set in a moment when action seems impossible. Arjuna wants to withdraw, and the teaching that follows asks how to act well in difficult situations. Its answers apply far beyond battlefields: how to work hard without anxiety, how to meet success and failure with balance and how to make ordinary effort a source of peace.
Gita 2.47 says we have a right to our action but not to its fruits, so put full effort into work while releasing anxiety about outcomes you do not control. Gita 2.48 defines yoga as acting in balance, free from attachment and unmoved by success or failure, and Gita 4.20 says freedom comes when actions are performed without dependence on their results. Gita 5.12 says peace comes from relinquishing attachment to outcomes, while craving specific results leads to bondage and anxiety.
The Gita also shows how action becomes spiritual. Gita 9.27 says every action, from eating to giving to austerity, becomes spiritual when it is consciously dedicated to the Divine, and Gita 5.10 says actions offered without attachment do not bind a person. Gita 6.1 says true renunciation is doing one's duty without attachment to its results, and Gita 8.7 says duty and remembrance are not opposed, so do your work wholeheartedly while keeping an inner connection to a higher purpose.