How to encrypt your disk using FileVault
FileVault allows to encrypt the disk of your macOS computer, thereby preventing people having physical access to your computer from reading your data. This is particularly important for laptops that can easily be forgotten or stolen. FileVault encrypts the whole disk and uses your password to unlock it during the early boot process. Once inside macOS, the user will not notice that his disk is encrypted.
FileVault can be activated anytime and will encrypt the data on your disk in the background. Chances that something can go wrong are tiny, but you should nevertheless make sure to have a recent backup before proceeding.
System Preferences -> Security & Privacy -> FileVault and press the button to turn it on.
Write down your private recovery key on a piece of paper and store it in a safe location.
Typically you want to choose not to store it on the Apple servers.
You will finally be prompted to restart your computer.
After the reboot, FileVault will start encrypting your disk. The time this process takes depends of course on the amount of data you have and whether you have SSD or not.
If you use TimeMachine you may optionally also encrypt your backups. Unless you are very paranoid (or have really sensitive data, or many people having easy access to your backup disk), we suggest to leave the backup disk unencrypted. This ensures that in the worst case scenario you can always access the data in your backups.