The rescue
When Poseidon shatters Odysseus’s raft, Leucothea rises from the sea in the form of a gull and speaks to him. She tells him to leave the raft, take off his clothes, and tie her veil under his chest; he will not drown while he wears it. She also warns him to throw the veil back into the sea once he reaches land.
Odysseus hesitates, suspecting a trick, but he follows her advice. The episode is a rare moment of divine help without a bargain or a test. Leucothea asks for nothing except the return of her veil.
The white goddess
Her mortal story—Ino, driven mad by Hera, leaping into the sea with her son Melicertes—lies outside the Odyssey. In the poem she is simply a benevolent sea-power who appears when Odysseus is at his most helpless.
After she helps him, she dives back into the sea and disappears. The poem does not explain why she helps, and that is part of the effect: the sea is not only hostile, and the gods are not only angry.