In a nutshell, a proxy group is a list that holds service accounts for one or more users. This is used for managing access permissions to project data.
Each user is provided has a unique proxy group, displayed in the user's profile page in Terra. This proxy group contains a user's login identity, alongside any service accounts FireCloud may make on their behalf.
As a Terra user, you should generally not need to think about your proxy group. You can share workspaces and the data they contain within Terra with any other user based on their login identity. However, if you want to share non-public data that is stored in buckets NOT associated with FireCloud workspace for the purpose of running FireCloud workflows, you must use the recipient's proxy group instead of their login username.