Last sync: After installing the spy application (client app) on the target device, every 30 minutes it will try to send the recorded data to the server. Last sync value indicated the last synchronized time (base on the target device's clock - timezone).
Next sync: In case the application still works well, this value (next sync) is estimated time for the next synchronization (base on the timezone of the target device).
If the value of next sync shows: (No response or waiting), maybe you should check if the application still works or not, or try to understand why the device is offline. There are many steps to check if the device is offline (the device does not have any connections to the server).