part of speech:  verb

definition: Cause (a fire or light) to cease to burn or shine.

Source: Oxford Dictionary

Found in the line 10 on “Field Trip to the Museum of Human History” by Franny Choi

The word “extinguish”  in the stanza means the nightstick stops or destroys the light in people’s eyes . I believe the hidden meaning of the sentence is that it breaks people’s dream, or hope for their future.