First, a note about Urban Dictionary. This accepts definitions from anyone on the Internet, with little or nothing in the way of quality control. Some contributors clearly compete to invent the most outrageous or absurd meanings, so you should never accept anything from Urban Dictionary without checking in other, more reliable, sources!
Second, the verb “melt” has the sense “to soften or weaken”, and this has long been used figuratively to describe weakening of resistance to love or sexual activity. The OED includes these senses:
melt, v. 3.b. intransitive. To become softened by compassion, pity, love, etc.; to yield to entreaty
e. intransitive. To become ecstatic; to yield to rapture or delight; spec. to experience sexual orgasm.
Oxford English Dictionary.
The OED quotes George Granville as an early example of sense e:
Achilles O how she clasps Atrides in her Arms!
So she hugg’d me, and with her darting Kisses
Met me half way, as now she meets his Lips.
How close she clings! and how with rapture melts!
George Granville (1698). Heroick Love, act II, scene I. In Four Plays of the Right Honourable the Lord Lansdowne (1732), p. 113. London: W. Feales.
So in milet’s song the speaker says that her resistance has melted like ice cream, and asks her lover not to “be shy”: that is, to have sex with her.
(In comments there was a suggestion, now deleted, that the melting ice cream is intended to suggest the speaker’s vaginal lubrication due to her sexual arousal: although this makes sense, I think the primary meaning is the weakening of resistance or disinclination to sexual activity, as in Granville.)