Adaptive traffic signal control (ATSC) is crucial in alleviating congestion, maximizing throughput and promoting sustainable mobility in ever-expanding cities. Multi-Agent Reinforcement Learning (MARL) has recently shown significant potential in addressing complex traffic dynamics, but the intricacies of partial observability and coordination in decentralized environments still remain key challenges in formulating scalable and efficient control strategies. To address these challenges, we present CoordLight, a MARL-based framework designed to improve intra-neighborhood traffic by enhancing decision-making at individual junctions (agents), as well as coordination with neighboring agents, thereby scaling up to network-level traffic optimization. Specifically, we introduce the Queue Dynamic State Encoding (QDSE), a novel state representation based on vehicle queuing models, which strengthens the agents' capability to analyze, predict, and respond to local traffic dynamics. We further propose an advanced MARL algorithm, named Neighbor-aware Policy Optimization (NAPO). It integrates an attention mechanism that discerns the state and action dependencies among adjacent agents, aiming to facilitate more coordinated decision-making, and to improve policy learning updates through robust advantage calculation. This enables agents to identify and prioritize crucial interactions with influential neighbors, thus enhancing the targeted coordination and collaboration among agents. Through comprehensive evaluations against state-of-the-art traffic signal control methods over three real-world traffic datasets composed of up to 196 intersections, we empirically show that CoordLight consistently exhibits superior performance across diverse traffic networks with varying traffic flows. The code is available at https://github.com/marmotlab/CoordLight