Concept-based eXplainable AI (C-XAI) aims to overcome the limitations of traditional saliency maps by converting pixels into human-understandable concepts that are consistent across an entire dataset. A crucial aspect of C-XAI is completeness, which measures how well a set of concepts explains a model's decisions. Among C-XAI methods, Multi-Dimensional Concept Discovery (MCD) effectively improves completeness by breaking down the CNN latent space into distinct and interpretable concept subspaces. However, MCD's explanations can be difficult for humans to understand, raising concerns about their practical utility. To address this, we propose Human-Understandable Multi-dimensional Concept Discovery (HU-MCD). HU-MCD uses the Segment Anything Model for concept identification and implements a CNN-specific input masking technique to reduce noise introduced by traditional masking methods. These changes to MCD paired with the completeness relation enable HU-MCD to enhance concept understandability while maintaining explanation faithfulness. Our experiments, including human subject studies, show that HU-MCD provides more precise and reliable explanations than existing C-XAI methods. Code will be available for research purposes upon acceptance.