Shield Platform Encryption gives your data a whole new layer of security while preserving critical platform functionality. It enables you to encrypt sensitive data at rest, and not just when transmitted over a network, so your company can confidently comply with privacy policies, regulatory requirements, and contractual obligations for handling private data.
Classic encryption lets you protect a special type of custom text field, which you create for that purpose. With Shield Platform Encryption you can encrypt a variety of widely-used standard fields, long with some custom fields and many kinds of files. Shield Platform Encryption also supports person accounts, cases, search, approval processes, and other key Salesforce features.
For implementation, check the below link
https://www.infallibletechie.com/2016/11/how-to-enable-platform-encryption-in.html
To know more, check the below link
Note:
Manage Encryption Keys – Permission to manage Shield Platform Encryption.
View Encrypted Data – Permission to view the encrypted fields.