In William Shakespeare's comedy-romance As You Like It, a melancholy lord named Jaques has chosen to live in the Forest of Arden with the banished Duke Senior, whose dukedom was usurped by his brother, Duke Frederick. In act 2, scene 7, Jaques gives a monologue to Duke Senior and the other nobles and lords who live in the forest with him which begins, "All the world's a stage, / And all the men and women merely players" (2.7.146–147), which has become known as the "Seven Ages of Man" speech.
In the monologue, Jaques describes the seven "ages" or seven stages of a man's life, from infancy to death, and compares them to parts or roles that a man might perform on stage in a play. It's not likely that a man would have much opportunity to play the first two roles on stage, that of an infant and a schoolboy, but the third through sixth parts are easily recognizable as the "stock" characters of the lover, the soldier, the lawyer or judge, and the foolish old man, which are well-known characters who appear in plays throughout theatrical history.
Jaques says the the third role that a man might play in his life is that of a lover.
And then the lover,
Sighing like furnace, with a woeful ballad
Made to his mistress's eyebrow. (2.7. 154–156)
The lover is played in As You Like It by Orlando, a young man who has fled to the forest to escape being killed by his evil brother, Oliver. Orlando is truly in love with Rosalind, who is Duke Senior's daughter and who has also been exiled to the forest, but Orlando expresses his love for Rosalind by composing poorly-written love poems to her and then posting the poems on trees throughout the forest, which directly corresponds with Jaques lines, "with a woeful ballad / Made to his mistress's eyebrow."
Jaques even makes mention of the widely-posted woeful poetry when he later meets Orlando.
JAQUES. I pray you, mar no more trees with writing love songs in
their barks. (3.2.266–267)
Jaques line, "Sighing like furnace," has multiple levels of meaning. The line can represent the sighs of the young man who is desperately, perhaps even hopelessly in love. In Orlando's case, Rosalind has no idea that Orlando is in love with her until she reads some of the poetry he's posted in the forest.
The line can also represent the hot-blooded passion that a lover feels for his beloved "mistress" or sweetheart, such as the unrestrained, passionate love that Romeo has for Juliet.
A third interpretation is that the line refers to the love songs that a young man might sing to his beloved. Orlando doesn't sing to Rosalind in the play. If the quality of Orlando's singing is anything like the quality of his poetry, this is probably a good thing. Nevertheless, there are many songs sung throughout the play which reflect Orlando's love for Rosalind, and Orlando is content to let other people sing them.