Both Peer-to-Peer Texting and Broadcast Texting results pages display the number of responses your text received. (These are contacts sending a response to the initial message you sent them.)
When contacts respond, threads are created in users' inboxes in the "volunteer" frontend interface of Impactive (accessible via web or mobile app).
There are several reasons why you might see that your text received responses, but you can't find any threads in your inbox:
Response threads are shown in the inbox(es) of the user(s) who the threads are currently assigned to. Keep in mind that you can always reassign the threads to a different user. Read more about how to reassign here.
For Peer-to-Peer Texting: This means that responses will go to the user who originally sent the initial message. If you don't see responses in your inbox, other users might see responses in their inbox, because the responses were sent to the contacts that they originally messaged.
For Broadcast Texting: Responses are split evenly among the users who are present on the responder list set for that broadcast text. If you aren't on the user list that was set as the responder list for that broadcast, you won't see any threads in your inbox - but users who were on the responder list will.
All of the responses were opt-outs. Note that the "Responses" metric listed on the results page includes opt-outs; so, if you see that your text received 5 responses, but also 5 opt-outs, it means that 100% of those responses were opt-outs. Most opt-outs are automatically tracked by Impactive and do not reach users' inboxes (more info here), so your inbox might be empty because there weren't actually any non-opt-out responses to be managed.
Another admin already reassigned responses away from you. Read more about reassignment here; you may want to check if a colleague has already reassigned threads away from you. If they did, you won't see threads in your inbox anymore.