Originally, the purpose of the chrisom-cloth was to keep the chrism, a consecrated oil, from accidentally rubbing off. With time, the word's meaning changed, to that of a white mantle thrown over the whole infant at the time of baptism.
The christening cloth's initial purpose was to safeguard the consecrated oil from unwanted transfer, but its meaning expanded to signify the white garment draped over the infant at the moment of baptism.