Drawing inspiration from the outstanding learning capability of our human brains, hyperdimensional computing (HDC) emerges as a novel computing paradigm, and it leverages high-dimensional vector representation and operations for brain-like lightweight machine learning (ML). Practical deployments of HDC have significantly enhanced the learning efficiency compared with current deep ML methods on a broad spectrum of applications. However, boosting the data efficiency of HDC classifiers in supervised learning remains an open question. In this article, we introduce hyperdimensional efficient active learning (<inline-formula><tex-math notation="LaTeX">$\mathsf{HEAL}$</tex-math></inline-formula>), a novel active learning (AL) framework tailored for HDC classification. <inline-formula><tex-math notation="LaTeX">$\mathsf{HEAL}$</tex-math></inline-formula> proactively annotates unlabeled data points via uncertainty and diversity-guided acquisition, leading to a more efficient dataset annotation and lowering labor costs. Unlike conventional AL methods that only support classifiers built upon deep neural networks (DNN), <inline-formula><tex-math notation="LaTeX">$\mathsf{HEAL}$</tex-math></inline-formula> operates without the need for gradient or probabilistic computations. This allows it to be effortlessly integrated with any existing HDC classifier architecture. The key design of <inline-formula><tex-math notation="LaTeX">$\mathsf{HEAL}$</tex-math></inline-formula> is a novel approach for uncertainty estimation in HDC classifiers through a lightweight HDC ensemble with prior hypervectors. Additionally, by exploiting hypervectors as prototypes (i.e., compact representations), we develop a sample acquisition strategy for <inline-formula><tex-math notation="LaTeX">$\mathsf{HEAL}$</tex-math></inline-formula> to select diverse samples within each batch for annotation. Our evaluation shows that <inline-formula><tex-math notation="LaTeX">$\mathsf{HEAL}$</tex-math></inline-formula> surpasses a diverse set of baselines in AL quality and achieves notably faster acquisition than many existing state-of-the-art AL methods, recording 12<inline-formula><tex-math notation="LaTeX">$\times$</tex-math></inline-formula> to 45,700<inline-formula><tex-math notation="LaTeX">$\times$</tex-math></inline-formula> speedup in acquisition runtime per batch.