In an investigation, the gaseous products of cellular respiration and combustion

Cellular respiration and combustion both produce carbon dioxide (CO2).

Carbon dioxide dissolves in water to form an acid (carbonic acid, which can then dissociate in water as an acid):
CO2 + 2H2O --> H2CO3 + H2O --> H3O+ + HCO3-

The reaction occurs to a small degree, but dissolution of CO2 will certainly make water more acidic.*

Bromothymol blue is a pH indicator, so when it becomes more acidic, it will turn yellow. Thus, it can indicate the dissolution of CO2 in water.

*You have probably heard about CO2 as a greenhouse gas. The other problem with CO2 emissions is ocean acidification. As more CO2 dissolves in the ocean, it becomes more acidic, which can harm organisms that construct shells or skeletons out of carbonates.