"PushSubscription" is an API on Exchange Web Services that allows to subscribe to push notifications. Attackers abuse it to make Exchange servers authenticate to a target of their choosing. The coerced authentication is made over HTTP, which is particularly powerful when doing NTLM relay (because of the Session Signing and MIC mitigations). As Exchange servers usually have high privileges in a domain (i.e. WriteDacl, see Abusing ACLs), the forced authentication can then be relayed and abused to obtain domain admin privileges (see NTLM Relay and Kerberos Unconstrained Delegations).
PrivExchange (Python) is a tool able to log in on Exchange Web Services and call that API.