Signing means attaching electronic signatures to e-mail messages or even software to prove its correct derivation. To keep someone else from writing messages using your name, and to protect both you and the people you send them to, you should sign your mails. Signatures help you easily check the sender of the messages you receive and distinguish good-natured messages from malicious messages.
Software developers sign their software so that you can check the integrity. Even if you get the software from an unofficial server, you can verify the package with the signature.
You might also have sensitive information you want to protect from other parties. Encryption helps you transform data and make it unreadable for others. This is important for companies so they can protect internal information as well as their employees' privacy.