Largely a cultural and devotional symbol, said plainly: the white lily (Lilium candidum, the 'Madonna lily') became the emblem of purity and especially of the Virgin Mary in Western art, where the angel Gabriel or Mary herself holds a lily at the Annunciation. Scripture's lilies are different plants in different settings — 'consider the lilies' (Matt 6:28), the lily of the Song of Songs (2:1-2), the lily-work of Solomon's temple (1 Kings 7) — and do not by themselves establish the later Marian symbolism.
Biblical references: Matthew 6:28-29 · Song of Songs 2:1-2 · Hosea 14:5 · 1 Kings 7:22-26
Meaning by Tradition
Catholic
The lily of purity and of the Annunciation: held by Gabriel in countless paintings, an attribute of the Virgin and of virgin saints (Joseph, Anthony of Padua). Easter lilies proclaim the resurrection.
Orthodox
Less central than in the West; floral purity imagery appears in hymnography, but the East's Marian symbolism runs more through the icon and the title Theotokos than through the lily.
Protestant
Kept close to the texts: Jesus' lilies of the field teach trust in providence; the Easter lily survives as a resurrection emblem. The Marian associations are treated as later devotional art, not doctrine.
A symbol made by art
The lily is the clearest case in this index of a symbol grown chiefly from devotion and painting rather than a proof-text. Scripture's various 'lilies' are different plants doing different work — providence in Matthew 6, love in the Song, ornament in the temple. The white Madonna lily as the badge of purity and the Annunciation is a Western artistic tradition, beautiful and old, but a tradition.
What it carries
Held by Gabriel, the lily says the conception is pure and the news is holy; set on an Easter altar, its white trumpet says the tomb is empty. 'Consider the lilies' anchors the humbler, surer note — the God who clothes the field will clothe his children. Theologos states the devotional origin plainly so the art is enjoyed for what it is.
Pastoral Caution
Don't read the developed Marian lily back into Scripture's lilies — they are different plants and different lessons. Enjoyed as devotional art it is lovely; treated as a biblical proof of later doctrine it overreaches.