Shade grass refers to any type of grass or combination of grass varieties that are shade tolerant.
Shade can range from partial shade (some sun during the day) to full shade (shady most of the day). Shade can also refer to dappled shade (light penetrating shady tree branches, and light or heavy shade (under varying tree canopies). Some grasses do better in varying degrees of shade.
The best cool season shade grasses are from the fescue family. Creeping red fescue is the best performer but is often blended with Hard fescue and Chewings fescue to easier adapt to varying degrees of shade and different soil types. Tall fescues also do well in the shade and it is not uncommon to find it in seed blends specialized for shade.
Each fescue variety contains many different cultivars, some preferred for their disease resistance, drought tolerance or soil adaptability. High profile cultivars will ramp up the cost and are mainly used in high-end applications like golf courses. A mid-priced cultivar should be fine for most shady lawns.
The best warm season shade grass is St. Augustine grass, but it cannot be bought as seed. It must be sprigged or planted as sod. Zoysia grass and Centipede grass are also decent shade grasses for southern climates, however, the more northern the lawn, the less these grasses will thrive in the shade. Closer to the transition zone, and including the transition zone, fine fescues are more suitable for shade tolerance.
A helpful tip is to try and minimize the shade by pruning/thinning out shady trees or even consider a shade loving ground cover like pachysandra. Sometimes it's just easier to use a plant that is more suitable for the location than grass.