This is one of a series of edifying subjects painted in a room of the Petrucci Palace in Siena in about 1509. Two others - 'The Triumph of Chastity' and 'Coriolanus persuaded by his Family to spare Rome', both by Signorelli - are also in the National Gallery. The paintings suffered damage when detached from the wall, hence their crumbly surface.
The woman at the loom is Penelope, wife of Odysseus, the hero of Homer's 'Odyssey'. During his long absence after the Trojan War she is besieged by suitors but refuses to consider their advances until she has finished weaving her father-in-law's shroud. However, she unpicks by night what she weaves by day. The men before her are presumably suitors. The man entering the room is Odysseus disguised as a beggar.
Other episodes in the poem are depicted in the distance: Odysseus listens to the song of the sirens strapped to the mast of the ship while his crew block their ears. Sailors in a small boat nearby dive into the water, maddened by the beauty of the singing. On the coast Circe meets Odysseus. Around him are the swine into which this sorceress has turned previous visitors.