The lining on a saddle is more comfortable for the rider as opposed to the grain of the leather which is harder and less comfortable.
There are two types of linings: calfskin and buffalo leather.
The difference comes mainly from the aesthetic style and the grip.
A saddle lined with calfskin will tend to have less grip when it is new but a little more after a few months of use.
On the other hand, a new saddle lined with buffalo leather will tend to have a lot more grip but it will form a patina over time, and so have a little less grip.