Swell factor refers to the amount that the volume of a block of material increases once it is removed from the ground. The block of material "swells" due to the fact that it breaks into smaller pieces. Before breakage, the block is consolidated; but after breakage, the pieces do not fit perfectly back together and so they take up more space.
The swell factor can be calculated from the in-situ and excavated volumes, or from the "bank" and "loose" density. Consider the figure below:
The material has the same mass before and after breakage, but the volume changes from V1 to V2. The swell factor = V2/V1 = (loose density/bank density).
Figure: When material is excavated, it swells.