A sparse matrix typically refers to a very large matrix of variables (features) and records (cases) in which most cells are empty or 0-valued.  An example might be a binary matrix used to power web searches – columns representing search terms and rows representing searches, and cells populated by 1’s or 0’s (presence or absence of the term in that row’s search).  Obviously most values are going to be 0 – each search will involve only a tiny minority of terms.  Computational methods can compress sparse matrices (taking advantage of the large expanse of 0-valued entries, which needn’t all be represented individually), rendering computation feasible for the large datasets required in web search prediction.