While "para" does indeed mean "beyond," I understand the concept of "paraliminal" by comparing it to what preceded it historically, "subliminal."

"Subliminal" refers to messages so low in intensity that one cannot make out what the messages are by focusing on what appears to be "noise" on the tape.

Contrariwise, "paraliminal" refers to messages sufficiently high in intensity that, if one focuses upon them, it is usually possible to make out what the messsages are saying.

best wishes,
Mike
moochy_hope@yahoo.com