All types of dispersion. tagwise is gene by gene, trend takes groups of similarily expressed genes to my knowledge, and common is aross the whole dataset. The BCV gives you a measure of how varied your biological replicates are. Generally around 0.4 or below is a good value to have.the BCV allows you to see the dispersion.
You can also do y$commondispersion etc to see your exact values. BCV is just the square root of this value.