Blind weaving means that the holes that hold the cane are drilled halfway through the wood so you can't see the loop of the cane on the backside.
Double blind caning is the same but the caning is repeated on the back or underneath side too. Double blind weave is like doing two chairs in one.
Blind caning and double blind cane are very labor intensive, and time consuming. Each and every strand has to be cut exactly to size, and then a drop of glue on the strand before being inserted into the hole, then a peg placed in the hold to secure that strand for drying. Generally this type of cane is used in high end antiques and museum quality pieces.