DISCLAIMER: Author is not an expert in cryptography (he is not an expert in anything really). Use this stuff at your own risk. If you find bugs or inaccuracies, please create an issue or PR on the github repository.
The GNU Privacy Guard, also known as GnuPG or simply GPG, is a popular open source OpenPGP (RFC4880) implementation. The system is widely trusted for securing integrity and confidentiality of internet communications through various cryptographic methods. GPG is used in Debian and Redhat to verify downloads from package managers (apt, yum) and people like Edward Snowden and Glenn Greenwald use it to encrypt confidential emails.
Like most modern crypto systems, GPG makes use of public key methods. You can easily generate a personal keypair which consists of a private key and corresponding public key.