From storyasking

[edit] why called barometer?

Barometer was just a word we coined for lack of a better word. The barometer is in theory the lowest motivated student. The main purpose of the barometer is to SLOW down the teacher. When the teacher focuses on the barometer and does frequent comprehension checks then the teacher will tend to talk slower, and make the lesson comprehensible to that person. This is a very important part of TPRS.

-Blaine

[edit] what are they thinking?

"barometer", "student", coincidentally, slightly coincides with an urban legend: http://www.snopes.com/college/exam/barometer.asp , summarized here:

teacher: "what steps would you take to determing the height of a building using a barometer?"

student: "i would lower the barometer on a string and measure the string."

from snopes: "The obvious moral here is that education should not consist merely of stuffing students' heads full of information and formulae to be memorized by rote and regurgitated upon demand, but of teaching students how to think and solve problems using whatever tools are available. In the mangled words of a familiar pharse, students should be educated in a way that enables then to figure out their own ways of catching fish, not simply taught a specific method of fishing."

lively discussion re: barometer on reddit