A substance with a density of 0.77 gm/cm^3 will float in water. The reason for this, is that the substance is "lighter," or less dense, than water. Water has a density of about 1 gm/cm^3 and hence is denser than the substance.
We can also describe this in terms of buoyancy. According to the Archimedes principle, the buoyant force acting on a substance is equal to the weight of the fluid it displaces. In this case, a density of 0.77 gm/cm^3 means that the substance has a mass of 0.77 gram per cm^3 of its volume. If we immerse 1 cm^3 of this substance, it will displace 1 cm^3 of water, which has a mass of 1 gm (Remember the density of water is about 1 gm/cm^3). So, we have an upward buoyancy force enough to support 1 gm and we have a downward force of only 0.77 gm substance. Hence the buoyancy will be able to keep this substance afloat in water.
Kindly note that the substance will only float in water if it is insoluble in water. Also, the substance will float in water or any other fluid with a higher density. If we immerse it in a liquid of lower density (say gasoline, with a density of 0.71 gm per cm^3), it will not float, but rather submerge.
Hope this helps.