Airwraps are a family of moves where the string of the poi wrap around each other and then unwrap.
This wrapping and unwrapping is caused by the angle that the poi collide at. The basic airwrap (as shown in the video linked below) occurs in front of the body.
Spin the poi in your left hand clockwise in the wall plane (flat in front of you).
Spin the poi in your right hand clockwise at about a 30 degree angle off the wall plane, with your hand slightly back.
Let the poi collide so that the right poi swings upwards into the descending left poi
The poi should spin once around where they collide and then separate. However it will take time to get this going smoothly enough. I find that lifting the right hand upwards slightly help the poi unlock.
Airwraps are possible with all poi, but some make it easier than others. Learning airwraps with tailed poi would be very difficult, whereas 'sock' poi are probably easiest. As airwraps are also part of glowsticking it seems that the weight of the poi heads doesn't matter too much, or rather is a personal preference. I find that heavier poi heads travel slower and with more momentum so give more control.
The word "hyperloop" was first used on this board by Glass in October 2002. Since then there has been constant debate about what a hyperloop actually is. Glass himself admits that he didn't fully know what the move was when he named it as a hyperloop. The definition of his hyperloop is:
An airwrap within a weave, starting with hands on top of each other on one side. The poi start airwrapping and transition to a beat of buzzsaw with the hands moving through 180 degrees of a circle (as in an isolation) so that the airwrap exits on the alternate side with the hands on top of each other, but reversed.
As with many poi moves there are many different definitions for a hyperloop brought about by the difficulty of understanding complex poi moves through text and a lack of clear video early on.
Ultimately a hyperloop is part of the airwrap family of moves and it doesn't actually matter what it is or what it's called as long as you're having fun.
More hyperloops, airwraps and random tangles are discussed on the forum, where Simian has compiled a list of good threads.