We use encryption very often, even if we don't use the details. When buying things online, hopefully you are using an SSL connection in your browser. SSL is Secure Sockets Layer, and uses encryption to secure your browser connection with a web site. If you use a password to log in to your PC, that password is stored encrypted on the hard drive. The password you enter when logging in is encrypted and compared with the stored version. VPNs and many Wi-Fi connections use encryption as well.
Privacy
The main use of encryption discussed here is clearly privacy. Only the intended audience (us or another party that has a key) can decrypt the information. If we encrypt our hard drive, if it is stolen the data on it is useless without a password and/or a digital key.
Validity
Encryption can also ensure that data has not been changed in transit or after it was stored. If we use a one-way hash any changes, even of a single bit in the source data, will result in a different output. When we compare the original hash with ours we can know the data has been modified.
Authenticity
Digital Signatures and PKI can be used to "sign" encrypted or plaintext documents and verify that the sender is who they claim to be. We use the public key to check the signature block created by the sender with their private key. Similarly we can use PKI for authentication for applications or network connections.
I hope this information helps you understand encryption in general and why it's so useful and important today.