Imitation learning (IL) is widely used for motion planning in autonomous driving due to its data efficiency and access to real-world driving data. For safe and robust real-world driving, IL-based planning requires capturing the complex driving contexts inherent in real-world data and enabling context-adaptive decision-making, rather than relying solely on expert trajectory imitation. In this paper, we propose CarPLAN, a novel IL-based motion planning framework that explicitly enhances driving context understanding and enables adaptive planning across diverse traffic scenarios. Our contributions are twofold: We introduce Displacement-Aware Predictive Encoding (DPE) to improve the model's spatial awareness by predicting future displacement vectors between the Autonomous Vehicle (AV) and surrounding scene elements. This allows the planner to account for relational spacing when generating trajectories. In addition to the standard imitation loss, we incorporate an augmented loss term that captures displacement prediction errors, ensuring planning decisions consider relative distances from other agents. To improve the model's ability to handle diverse driving contexts, we propose Context-Adaptive Multi-Expert Decoder (CMD), which leverages the Mixture of Experts (MoE) framework. CMD dynamically selects the most suitable expert decoders based on scene structure at each Transformer layer, enabling adaptive and context-aware planning in dynamic environments. We evaluate CarPLAN on the nuPlan benchmark and demonstrate state-of-the-art performance across all closed-loop simulation metrics. In particular, CarPLAN exhibits robust performance on challenging scenarios such as Test14-Hard, validating its effectiveness in complex driving conditions. Additional experiments on the Waymax benchmark further demonstrate its generalization capability across different benchmark settings.