No, it's not a hairdo or a square dance. It might be a square dance, but not in this instance.
It's a method I learned from my time at Johnson's Backyard Garden to support indeterminate tomatoes. Turns out I had a volunteer tomato plant last year that was indeterminite. A quick overview of the definition is: Indeterminate varieties of tomatoes are also called "vining" tomatoes. They will grow and produce fruit until killed by frost and can reach heights of up to 10 feet although 6 feet is considered the norm. They will bloom, set new fruit and ripen fruit all at the same time throughout the growing season.
In other words, they get ginormous. They will take over like the plant in The Little Shop of Horrors if you don't do something to rein them in.
The Weave is simply a way of supporting them on both sides. If you click on all these pictures, you'll see two things that are important.
1. The tomatoes need to be planted in a straight line.
2. There needs to be a support stake in the middle of two tomato plants.
All you have to do is wind the twine around one end, carefully beside the first tomato plant, around the center support, beside the second tomato, around the other support, and then do it all over in reverse. You'll need to do it several more times as they grow.
A bit of trivia---all heirloom varieties of tomatoes are indeterminate, BUT not all indeterminate tomatoes are heirloom. Confused? No worries. I'm that way most of the time.
Hybridization helped produce a more well behaved plant with greater production of a "perfect tomato".