Sometimes driving and parking on the grass cannot be avoided. If it only happens once in a while, and the soil is not overly moist, then there may be very little affect on the grass. However, driving on the grass too much can damage the lawn.
Some grass is more tolerant to being traveled on. Perennial ryegrass is better suited to be traveled on over varieties like Kentucky bluegrass and fine fescue. Perennial ryegrass has a very high wear tolerance. Tall fescue is also very wear tolerant, but its wide leaf blade sticks out in typical home lawns, and can be considered a weed because of it. But there are lawns that are all tall fescue that are very wear tolerant and looks aesthetically pleasing because of the uniform look.
Even though some grass varieties are more wear tolerant than others, soil with clay in it is more likely to compact. If the clay becomes too compacted, the roots will not be able to grow, or pick up moisture and nutrients, and the grass will struggle to grow, then eventually die off. There is a way to help to counteract the compaction, aerating your lawn can help. It will take time for the compaction to be alleviated, but overtime it will come, as long as it is not continuing to be traveled on.
If driving in that spot is unavoidable, then installing a paved surface may need to be an option. However, if the look of the property, or because of zoning reasons, you want or need to keep the grass, there is still an option to help keep the grass alive. There is a product out on the market that is designed to carry the weight of the vehicle without compacting the soil. A porous grid is installed underneath the soil where you want to drive, but the grass can grow in the holes of the grid. The grid carries the weight, and the grass is protected.
It is best to avoid driving on the grass, but if it is unavoidable, there are options. Choosing perennial ryegrass and installing a compaction grid will help. So there are options to have the nice lawn, and an that extra parking spot when needed.