This Hymenocallis species, most likely Hymenocallis littoralis (ht 75-90 cm), given to me many years ago by an elderly gardening friend, has stout stems of large, scented, crisp white flowers: with long spidery petals around a daffodil-like cup and prominent, quivering stamens. Hymenocallis come from Central and South America and the Caribbean region, and begin to bloom at Christmastime and continue into January. The clumps of strappy evergreen leaves, rather like the foliage of Agapanthus, are attractive for the rest of the year, though sometimes succumb to a rust-like disease, in which case I just cut them all off and they regrow.
Belonging to the Amaryllidaceae family of bulbs - many of which do very well in our Sydney gardens - they form thick clumps, and though mine are grown in full sun, they will also do well in shade (including heavy shade), though flowering a bit later and less profuse than those growing in sun. They can also thrive in very boggy soil as well as well-drained spots. I have seen them growing well in the sandy soil of a seaside garden. They can be grown in pots. In short, they are most adaptable plants! They form robust clumps; from my original bulb I have had huge clumps that I have been able to give away to other gardeners over the years! The sharp whiteness of the flowers contrasts well with a sultry background of purple leaves: mine are nearby Persicaria 'Red Dragon' and an unusual shrubby spurge - Euphorbia cotinifolia (ht 3m) - and for a while they nestled amongst the dark blooms of Hemerocallis 'Black Ambrosia', to striking effect. The drooping petals echo the arching leaves of grasses grown nearby, and they are particularly effective with Miscanthus 'Variegatus', which has white-striped leaves.
The plants have few pests but can be attacked in spring by the scary black and yellow striped amaryllis caterpillars (also known as the lily borers), which can cause a lot of damage to the whole plant in a very short time. They should be dealt with promptly, using a product such as Success, Dipel or a pyrethrum spray. They can also be picked off by hand and squashed! Snails can also lurk under the leaves so check for them every so often.