A scientist immerses an irregularly shaped object into a beaker of water and notes how far the water rises.What property of the object is the scientist measuring?

The amount the water rises is dependent of the volume of water displaced by the object - thus it can be used to measure the volume of the immersed object. If the object did not immerse completely - if it floated - the displaced fluid could instead be used to calculate the relative density of the object - when combined with the total volume.