When you install Whospair, your phone creates a key pair and gets its own Tor onion address. That key is your identity. To add someone, you scan each other's QR code, ideally in person.
From then on, your phones talk directly. If your contact's app is closed, the message waits on your phone until it's open again. Nothing waits on a server, because there isn't one.
Turn the phone face down and the screen goes black. With the optional camera shield, it also hides when you look away or someone looks over your shoulder.