Encryption is the future of data security. It can be used to store your data in a way that it can only be read by yourself (or those having the private key), and not by others that have access to the data. And it allows to communicate with others in a way that only the conversation partners can read what is said, not the servers that forwards the communication.
Encryption is also used by servers to securely communicate with clients (such as your phone and PC) and other servers, using the SSL protocol (when combined with HTTP, widely known as HTTPS). This form of encryption effectively prevents eavesdropping, but it does not provide security against hackers, governments and malicious internet service providers.
The best way to implement end-to-end encryption for email is using Pretty Good Privacy (PGP). PGP works only if both you and your email partner have installed the required software and you have shared your public keys. There are various plugins for email applications that implement PGP. In Thunderbird, you can use the plugin Enigmail. For Outlook, you can use Gpg4win.
PGP is also supported by the webmail client. For this to work you first need to install the browser plugin Mailvelope, and import your PGP keys (or create new keys) into Mailvelope. See this page for some configuration instructions.
To read encrypted mail, you may need to change a setting in Roundcube. Go to Settings -> Preferences -> Encryption. Then turn on "Enable message decryption".
Roundcube also has a builtin PGP system, but I recommend against using it because it runs on the server, and hence is not true end-to-end encryption. However, the benefit of the builtin system is that you don't need to install the Mailvelope plugin to use PGP features.
Client-side storage encryption
Client-side encryption of stored emails is not currently supported.