In order to download a recording (could be a recorded outbound call, a voicemail recording, a recorded conference call, etc), just click the "Download" icon at the far right side of any audio player player bar after clicking on an activity item to expand it.

At this point, some browsers will open the file in an audio player instead of initiating a download. Simply go to "File" (or right click) -> "Save Page As" in your browser to initiate a download.