In Bible times, many containers for liquids as water, olive oil, and wine made from the skins of animals, particularly young goats. After the head and feet were cut off, the skin was stripped in one piece from the animal’s body. These skin retained the shape of the animal, with the neck sometimes serving as the channel through which the container was filled and emptied.
In this verse Jesus referred to those skin containers to show that the old age of the law was not compatible with the new age of grace that He brought to the world. Just as old, brittle wineskins would burst under the process of fermenting new wine, so His new age of grace demanded a radical departure fro the traditions of the past.
MATTHEW 9:17- Neither do men put new wine into old bottles [wineskins, NIV]: else the bottles [skin, NIV] break, and the wine runneth out, and the bottles perish [wineskins will be ruined, NIV]: but they put new wine into new bottles [wineskins, NIV], and both are preserved. both are preserved.