The Basics
What does a polygraph measure?
A polygraph does not directly measure whether a person is telling the truth. Instead, the instrument records physiological changes that can occur while a person answers a structured series of questions. The examiner considers the recorded data together with the examination procedure and the subject's responses.
The instruments I have experience with can record several channels, including respiration, electrodermal activity, cardiovascular activity, and movement/activity.
Respiration
Usually recorded with pneumograph sensors around the chest and/or abdomen.
Electrodermal Activity
Records changes in skin conductance.
Cardiovascular Activity
Typically recorded with a cardiovascular or blood-pressure cuff.
Movement & Activity
Records gross and subtle movement and can help identify physical activity or countermeasures.
A Brief History
From early recording devices to modern computerized instruments
The development of polygraph testing grew from earlier efforts to record physiological changes. In 1921, California police officer and physiologist John A. Larson developed an instrument capable of simultaneously recording blood pressure, heart rate and respiration. Leonarde Keeler later refined the technology and helped establish the practical use of the polygraph.
By the mid-20th century, polygraph instruments had evolved to include additional physiological channels and more practical recording systems. Modern computerized instruments continue the same basic concept while providing digital recording and analysis.

Important Context
A polygraph examination is a professional assessment, not a magic truth machine
Polygraph results should be understood in the context of the examination procedure, the questions asked, the recorded physiological responses, and the examiner's analysis. No instrument can simply read a person's thoughts or directly detect a lie.