In chemistry lime water can be used to test the presence of carbon dioxide because lime water reacts with carbon dioxide to produce a precipitate of calcium carbonate. It is used to show how Limewater + Carbon Dioxide Chalk(/Limestone) + Water :
Ca(OH)2(aq) + CO2(g) CaCO3(s) + H2O(l)
NB: If too much carbon dioxide comes into contact with the cloudy limewater, it will cause the calcium carbonate precipitate to redissolve to form soluble calcium hydrogencarbonate.
CaCO3(s) + CO2(g) + H2O(l) Ca(HCO3)2(aq)
If you want to remove large amounts of CO2 there are other more robus methods (but less useful as a test)