The wording leaves a lot to be desired, in my opinion. Where did you get it? Per Wikipedia:
"Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces".
The first statement makes no sense since mass is not weight.
The second statement also doesn't make sense because it doesn't necessarily have anything to do with buoyancy. For example, I can forcibly keep the object submerged in which case the volume of the water displaced will obviously equal the volume of the object. But if I have to forcibly hold it down, if I let the object go it would pop up an float partially.
The degree to which an object will float, either partially or completely, will depend on its density relative to the fluid. In order for the object to float (be in equilibrium), its weight must equal the weight of the volume of water it displaces. That is, the upward buoyant force exerted by the liquid on the object has to equal the downward weight of the object. Mathematically
The subscript $o$ indicates the volume and density of the object and the subscript $l$ the volume and density of the liquid.
The left side of the equation is the total weight of the object. $V_o$ is the total volume of the object, not necessarily the submerged volume of the object. The right side of the equation is the upward buoyant force exerted on the object. $V_l$ is the volume of liquid displaced by the submerged volume of the object.
If the densities of the object and liquid are the same, the upward buoyant force will exactly equal the total weight of the object, i.e., the object will float completely submerged.
If the density of the object is greater than the density of the liquid, the equality does not hold because the weight of the object will be greater than the upward buoyant force and the object will sink.
If the density of the object is less than the liquid, the object will float partially submerged. The submerged volume of the object will equal the volume of the liquid displaced, or
Hope this helps.