Polystyrene tiles were fashionable in the 1970s and 1980s. They were used for thermal insulation reasons, to conceal defects in ceilings and were regarded as being attractive to look at.
Whilst newer polystyrene tiles contain a flame retardant additive, many older ones do not and are a fire hazard. They should be removed. You should be prepared to undertake repairs to the ceilings hidden behind once removal has taken place.