OpenSSL is a free and open-source cryptographic library that provides several command-line tools for handling digital certificates. Some of these tools can be used to act as a certificate authority.
A certificate authority (CA) is an entity that signs digital certificates. Many websites need to let their customers know that the connection is secure, so they pay an internationally trusted CA (eg, VeriSign, DigiCert) to sign a certificate for their domain.
In some cases it may make more sense to act as your own CA, rather than paying a CA like DigiCert. Common cases include securing an intranet website, or for issuing certificates to clients to allow them to authenticate to a server (eg, Apache, OpenVPN).