Astigmatism is when the shape of the front surface of the eye or the lens inside the eye looks more like a football than a baseball.
Why a football? There are two different curvatures, 90 degrees apart or perpendicular to each other.
Why is this a problem? When light travels through a surface like this, the light is focused into different planes. Therefore, the person cannot focus on the object. Similar to an old autofocus camera that become confused and would not be able to focus onto an object.
A toric contact lens is made to compensate for this irregular shape. The lens will rotate and sit in a position to make the light focus onto one point, the macula. Different companies use different designs to stabilize the contact lens on the eye in order to bring you the sharpest vision.