"Independent" means that a change in the other factor does NOT produce any change in the factor of interest.
Changing the temperature of a mass or its environment does NOT change the mass. Thus, mass is independent of temperature.
At a constant pressure, increasing the temperature will increase the volume. This is seen most dramatically in gases, but affects solids and liquids as well. Thus, volume is dependent on temperature.
Density is a combined property. It is mass divided by volume. Although the mass is independent of temperature, the volume is not, as we have just seen. So, the combination of the two is still dependent on temperature due to the volume factor.
I would try a simplicistic explanation...
Mass is the amount of "stuff" (as in particles) of an object regardless of its dimensions.
Volume is basically the space occupied by the object and it depends upon the relative positions of the particles; if they vibrate a lot (hot stuff) the particles occupy more space!!!!
Imagine a class of students; the number of students is fixed (mass) but they can stay all sitting down (cold) or running around (hot) taking up more space inside the room.
Density is the ratio
Hope it helps!