When setting up security for linked servers, what does the Impersonate checkbox do?
Impersonate
Pass the username and password from the local login to the
linked server. For SQL Server Authentication, a login with the exact
same name and password must exist on the remote server. For Windows
logins, the login must be a valid login on the linked server.
To use impersonation, the configuration must meet the requirement for
delegation.

Create Linked Servers (SQL Server Database Engine)
In other words, this option corresponds to code
EXEC master.dbo.sp_addlinkedsrvlogin @rmtsrvname = N'remote_server', @locallogin = N'domain\account', @useself = N'True'