When a race car isn't handling well, the team depends on the driver to communicate the problem to the crew chief so that adjustments can be made during pit stops. Handling is judged by how well a car gets into and out of the turns. Obviously, the better the car handles, the faster the driver can go.
When a driver reports that his car is tight, it means that the car is not turning well and that traction in the front is poor. This is also known as understeer or pushing.