Human intelligence possesses the ability to effectively focus on important environmental components, which enhances perception, learning, reasoning, and decision-making. Inspired by this cognitive mechanism, we introduced a novel concept termed relevance for Human-Robot Collaboration (HRC). Relevance is defined as the importance of the objects based on the applicability and pertinence of the objects for the human objective or other factors. In this paper, we further developed a novel two-loop framework integrating real-time and asynchronous processing to quantify relevance and apply relevance for safer and more efficient HRC. The asynchronous loop leverages the world knowledge from an LLM and quantifies relevance, and the real-time loop executes scene understanding, human intent prediction, and decision-making based on relevance. In decision making, we proposed and developed a human robot task allocation method based on relevance and a novel motion generation and collision avoidance methodology considering the prediction of human trajectory. Simulations and experiments show that our methodology for relevance quantification can accurately and robustly predict the human objective and relevance, with an average accuracy of up to 0.90 for objective prediction and up to 0.96 for relevance prediction. Moreover, our motion generation methodology reduces collision cases by 63.76% and collision frames by 44.74% when compared with a state-of-the-art (SOTA) collision avoidance method. Our framework and methodologies, with relevance, guide the robot on how to best assist humans and generate safer and more efficient actions for HRC.