What determines an object’s ability to float?

Simply put, density is how tightly “stuff” is packed into a defined space.

For example, a suitcase jam-packed with clothes and souvenirs has a high density, while the same suitcase containing two pairs of underwear has low density. Size-wise, both suitcases look the same, but their density depends on the relationship between their mass and volume.
Mass is the amount of matter in an object.
Volume is the amount of space that an object takes up in three dimensions.

Density is calculated using the following equation: Density = mass/volume or D = m/v.

If something is heavy for its size, it has a high density. If an object is light for its size it has a low density.

The relative densities of an object and the liquid it is placed in determine whether that object will sink or float.