Asymmetric encryption is used to implement PKI. PKI is one of the most popular and reliable ways to manage encryption keys for an organization. All the participants trust a central trusting authority called a CA. CAs verify the identity of individuals and organizations and then issue them digital certificates (a digital certificate contains a copy of a person or organization's public key and its identity), verifying that the public key associated with that individual or organization actually belongs to that individual or organization. 

The way it works is that the CA asks a user to prove their identity, with different standards followed for individuals and organizations. This could involve simply verifying ownership of a domain name, or it could involve a more rigorous process that involves physical proof of identity, depending on the type of digital certificate that a user is trying to obtain. If the CA is satisfied that the user is indeed who they claim to be, the user then provides the CA with their public encryption key over a secure channel. The CA uses this information to create a digital certificate that contains information about the user's identity and their public key. This certificate is digitally signed by the CA. The user can then show their certificate to anyone who wants to verify their identity, without having to send it through a secure channel, as the certificate doesn't contain any sensitive information itself. The person receiving the certificate does not have to verify the user's identity directly. That person can simply verify that the certificate is valid by verifying the CA's digital signature, which validates that the public key contained in the certificate does, in fact, belong to the individual or organization named on the certificate.