The rapid adoption of cloud computing has transformed the way organizations store, process, and share data. However, outsourcing sensitive data to third-party cloud providers raises major security and privacy concerns, particularly in domains such as healthcare, finance, and government services. Traditional encryption schemes, while effective for secure storage and transmission, require data decryption for computation, exposing sensitive information to potential breaches. Homomorphic Encryption (HE) offers a promising solution by allowing computations to be performed directly on encrypted data without revealing its contents. This paper explores the principles of homomorphic encryption, its classification into partial, somewhat, and fully homomorphic schemes, and its application in enabling privacy-preserving cloud services. A conceptual framework is proposed for integrating HE with cloud-based data analytics and machine learning workflows, ensuring both functionality and confidentiality. Furthermore, we highlight current challenges such as computational overhead, key management, and scalability, while identifying future directions for efficient and practical deployment.