This is a species of Liriope, a tough little perennial (ht 30-60 cm) that grows as an arching clump of shiny, slim, evergreen leaves and is happy to grow in dry, shady spots, although will also cope with some sun. It is classified as belonging to the family Asparagaceae. It flowers in February and March, sending up little spikes of tightly clustered bell-like blooms. One popular cultivar is 'Silver Dragon' (or more correctly 'Gin-ryu', which I have never seen it actually sold as), with greyish-green leaves with a white stripe. It has pale lilac flowers. This looks effective growing with silver foliage plants such as Plectranthus argentatus, or with white-flowered specimens such as white hellebores or snowflakes to echo its white leaf stripes. This species is more inclined to spread, as it has a rhizomatous growth habit, and is sometimes referred to as the creeping turf lily.
All Liriope plants may produce black berries in autumn after the flowers fade. The foliage can become a bit shabby over winter, especially in colder regions, and apparently can be cut off (or even mown over!) in late August and new leaves will grow to replace the old. Propagation is by division of the clumps. The plants are frost hardy.