Alfirin was an Elvish name for the flower Men called simbelmynë (they also used the name uilos for the same flower). The name comes from its habit of growing thickly on the tombs of Men: it was found among the Kings' mounds in the Barrowfield of Edoras, and also on the Tomb of Elendil. The flower is described as being bell-like in shape, and could appear in many soft shades, though white seems to have been the most common.
An Elvish name meaning 'immortal'
In his comments in Unfinished Tales, Christopher Tolkien points out that Legolas' description of 'golden bells ... of mallos and alfirin', isn't quite in harmony with other descriptions, and he suggests that this particular use of the name may refer to a different flower altogether. Alternatively, the golden flowers of Lebennin might simply be a differently-coloured variety of the white alfirin commonly seen on Men's tombs.