Per Salesforce documentation, 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. Shield Platform Encryption builds on the data encryption options that Salesforce offers out of the box. Data stored in many standard and custom fields and in files and attachments is encrypted using an advanced HSM-based key derivation system, so it is protected even when other lines of defense have been compromised.

There are certain platform limitations that prevent us from fully supporting this feature.

Certain standard / custom fields are not eligible to by encrypted, specifically those which are referenced in the WHERE, GROUP BY, or ORDER BY clauses in a SOQL query. For example, if you're are using Case Merge Premium to identify duplicate cases and include the Subject field in your duplicate criteria, you will not be able to encrypt Subject as it's being utilized in the WHERE clause of a SOQL query.

Additionally, Salesforce will prevent AppExchange applications from being installed if there are existing encrypted fields in your organization that need to be referenced in the SOQL queries of a packaged component.

Some additional information / limitations on encrypting fields can be found here.