In Text 13 Krishna said, tasya kartaram api mam viddhy akartaram - "Although I act, I do not act." In this text, Krishna clarifies the meaning of these zen-like words.
The Sankrit word karma means both "action" and "reaction," as the two are almost inseperable in Vedic thought. (The word also means "duties," the religious actions one performs to achieve desired reactions.) Krishna is the karta, the doer, because he acts, he does things. However he is akarta, the non-doer, because his action is free from reaction (na mam karmani limpanti).
How can one engage in action without being affected by the reaction? Krishna explains, na me karma-phale spriha. Almost everyone acts or works for a specific purpose - they want to enjoy the fruit of their work. Those who work in this way will enjoy the fruit, be it bitter or sweet. But those who work work out of duty and are not interested in enjoying the fruit will not have to "enjoy" the bitter-sweet fruit of material existence.
I might ask you to pick my neighbor's flowers. Upon being caught, my neighbor may become angry with you. However, when you inform his that I told you it was ok to do so, his anger will quickly withdraw from you and focus upon me. Since it was not your desire that motivated the action, the reaction does not come to you. One who does not act out of desire to enjoy the fruits will not recieve an entangling reaction to his work.
Krishna, being the Supreme Lord, certainly has no needs to fulfill within this limited material world. Thus his actions, unmotivated by desire, are free from the bondage of reactions. One who knows this about Krishna will strive to also rid his work of selfish motive. As he acts out of duty - for the sake of pleasing the keeper of duty, God - he too becomes freed from the reactions of his work and achieves liberation.