Stability dictates the Stamina that is drained whenever one is hit when blocking and thus determines how long one can continually block while receiving blows.
The reduction to stamina drain is percentual, with one point of stability being equal to one percent of reduction. As such, 60 stability will reduce all incoming stamina drain by 60%, this goes up to the hard cap at 100 stability, which completely negates all stamina drain.
Certain classes of shields and weapons have higher stability than others. Greatshields are known for having the highest stability out of the shields, with the highest being a Crystal Tower Shield, while Ultra Greatswords have the highest out of the weapons.
While reinforcing a shield usually increases its stability, some shields only have their damage increased. Only gaining an increase in damage mostly occurs on Unique Shields.
Apart from reinforcing, stability can be increased with the Magic Shield & Strong Magic Shield sorceries. Both sorceries last for 15 seconds (~22 with the Lingering Dragoncrest Ring) and grant an additional stability of 18 and 34 respectively. This allows any shield with 82 stability to negate all stamina loss, and the strong version will do the same for shields with as little as 66 stability.