Origin of the proverb is from "Travel History": Sending a swan feather from a thousand miles, though the gift may be light but the feelings are deep.
Interpretation:The gift is small but affectionate.
There was a local official who by chance got a rare bird - a swan, so he sent a trusted aide named Mian Bo Gao to take it to the emperor as tribute. As Mian Bo Gao was carrying the swan, when he arrived at the Pan Yang Lake, suddenly he felt that he should stop to give the swan a bath, so he carefully placed the swan into the water. Suddenly, the swan spread its wings and flew away, leaving behind only a single feather. Mian Bo Gao had no way to catch it, so he could only take the swan feather to see the emperor.
Mian Bo Gao feared that the emperor would punish him, so he compiled a jingle, which in effect is this: "I came to give tribute to you, after crossing a thousand mountains and rivers, but at the Pan Yang Lake the swan flew away; I am very saddened, now standing before the Son of Heaven, I plead for forgiveness for myself. Besides, I am sending a swan feather from a thousand miles, though the gift may be light but the feelings are deep." After the emperor listened to this, he spared Mian Bo Gao.