The upward-pushing force that keeps things afloat is called buoyancy. For an object to float it must be able to equal its own weight by displacing enough water. A life jacket is mainly filled with gas which has a very low mass. As such when worn by a person, it acts to significantly increase their volume for only a very small increase in their mass. This means that they have a lower density than normal which increases their buoyancy and helps them to float.
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