The unwrap & recapture is a very basic move that will come up in many other more advanced diabolo tricks, it is also a useful way of getting into & out of some other moves as well.
Start the diabolo spinning. Then feed the string in from one side, by this I mean raise one handstick & lower the other so that the string is longer on one side of the diabolo than it is on the other. If you raise your left handstick, you are feeding the string attached to the right handstick into the diabolo.
You should be standing with the diabolo spinning in its normal position with one arm in the air & the other hand close to the diabolo. Now in one quick move tug the lower handstick to cause the diabolo to hop straight up a little way, then circle the lower handstick down & underneath the diabolo so that it leaves the string (that's the unwrap). Continue the circle around, up & over the diabolo. As you start the downward part of the circle, make sure the string is tight by raising the arm in the air a bit further. Then keep going & circle the handstick back underneath the diabolo, wrapping the string underneath the axle to catch the diabolo as you go (that's the recapture). After the recapture it is important to remember to lift the handstick above the diabolo otherwise it will either fall off the string or roll down & collide with the stick!
In a nutshell all you are doing is circling your handstick around the diabolo twice, once to take the string away, then once more to catch it again.
After unwrapping & recapturing you will find yourself with your arms/string crossed. To get back to your starting position perform another unwrap & recapture with the same hand, but this time circling the other way. Practise this move both ways with both hands.
You can also exit an unwrap & recapture by making a Crossed Arm Throw, remembering that the hand you recaptured with goes underneath. After learning this trick you may like to have a go at Unwrap & Recapture half turns.