You have two options to put the recording files into your Dropbox account.
First option: Manual upload. Make sure you have your Dropbox installed on your phone and signed in. To share the recordings, simply press Share and choose Dropbox.
You can add multiple recordings to Dropbox, and Dropbox will handle the uploading automatically. Long-press on the recording list to select more than one item, then press the share button to add to Dropbox.
Second option: Automatic upload. Use the Dropbox Auto-Upload feature introduced in version 2.1 of Hi-Q MP3 Voice Recorder. Go to app Settings (tap the gear icon) and select Dropbox. Once you are signed in, you can choose to automatically upload your recordings to Dropbox. Recordings will be uploaded to Apps > Hi-Q Recordings folder on your Dropbox.