How do you calculate how dense or sparse a dataset is?
It's actually defined on the first page:


  ... sparsity level (ratio of observed to total ratings) ...


In other words, the fraction of the user/item rating matrix that is not empty. Remember that the problem is that most user-item pairs have no rating, and we wish to estimate them.

Example:

Let there be three users and four products. The number of possible ratings is $3\times4 = 12$. If every user rates only one product each (regardless of which product), the density is 3/12 = 25%.