Triple pleat curtain is a type of header that is used on the top of curtains, in the same way, there are eyelet curtains and pencil pleat curtains, there are pleated curtains.
The simplest way of thinking about it is the curtains are pinched at the top along the header.
At Livingstone textiles when we make pinch pleat curtains we tend to make them with buckram, buckram is a very stitch interlining that is ironable on one side, this is a more traditional way of making them. The buckram gets sewn between the curtain material and the lining and is used to stiffen the top. The top where the buckram is placed is then pinched and sewn to create a beautiful even pinch at the top. They effect can also be gained with a pinch pleat header tape that is sewn along the top of the curtain in the same way standard header tape is used.
This same process is used to create triple pleat curtains and double pleat curtains.