There are several different formats that can be used to hold sparse arrays. Each has its own advantages and disadvantages. Mathematica uses the Compressed Sparse Row (CSR) format as an internal storage format. This can be explained for a sample matrix shown below.

In[1]:=

Out[2]//MatrixForm=

You can see the internal form in the InputForm of the matrix.

In[3]:=

Out[3]//InputForm=

This format is general enough to describe arbitrary rank tensors. Other advantages of the format include the fact that data elements in the same row are stored next to each other, which leads to better cache performance. A disadvantage is that it is not optimized for inserting new elements into the matrix.