This is an allusion to the Book of Exodus from the Bible. In it, the Pharaoh is threatened by 10 plagues unless he lets the imprisoned Israelites go. The last of the plagues is the death of the first-born son. First born refers to Duke Frederick, the elder of the two brothers.

Here, Jaques means that “ducdame” is an invented word that only fools would try to parse. It “draws fools into a circle” because fools would sit around discussing what it meant rather than recognizing that it was gibberish.

While Amiens sings a romanticized song about being exiled to the forest, Jacques’ verse is a cynical take on the pastoral song. He imports realism into the pastoral trope and mocks the tradition of the pastoral. While the pastoral attempted to create an edenic paradise within nature, the reality of the countryside, and these characters’ place within it, was much less ideal. Jaques uses his pastoral song to challenge the idea that these nobles are better off in Arden away from the city.

The pastoral song generally appeared when it was thematically apt and disappeared after it had run its course, much like a song in a musical. However, here Jaques interrupts this trend to demand the player keep singing. Jaques leverages his social power to force Amiens to perform the pastoral; in essence, he ruins the pastoral by bringing his urban perspective into the forest space.

Pastoral songs are a motif of pastoral literature. They generally took the form of folk songs performed with flutes or lutes, and used simplistic images to paint an idyllic scene. The harmonies of the song underscored the harmony thought to exist in the pastoral landscape, while the presence of singing within a story represented the carefree life of those who had the time and space to sing.

Jaques’ cryptic song mentions a man “turn[ing] ass,/Leaving his wealth and ease.” The image of a man turning into an ass alludes to King Midas, a figure in Greek mythology. After being given the ability to turn anything to gold with his touch, Midas renounced his wealth and became a disciple of Pan, the nature god. When asked to judge a musical competition between Apollo and Pan, Midas selected Pan as the victor. In a rage, Apollo gave Midas donkey’s ears. It is unclear precisely why Jaques evokes Midas, though the story does include multiple parallels. The musical competition in the Midas story mirrors the song competition between Jaques and Amiens. Midas’s choice to renounce worldly goods and become a disciple of nature mirrors Jaques’s character, devoted as he is to the natural world.

A scholar has recently speculated that the phrase might be a combination of *Duke *and Dame, Jacques' sarcastic way of reminding Duke Senior that he gave up his kingdom like a woman, that is, without a fight.  This may be Jacques' way of expressing his displeasure at having to rough it in the forest instead of living comfortably at court (had the Duke fought for his kingdom).

This is a reasonable interpretation given the beginning of Jacques' speech in which he chides the Duke for "leaving his wealth and ease/A stubborn will to please."

In the play, the word is stanzo, not stanza.  Jacques is most likely pretending not to know the correct word.

This is a visual joke. When Jacques sings, "Ducdame, ducdame, ducdame," all the other men gather around him in a circle, drawn by curiosity. So Jacques is saying that they are a bunch of fools and he has called them into a circle with his strange word. "Ducdame" should be pronounced as three syllables (whatever it may mean, if anything).

In Exodus 12, God caused the death of the first born of all the Egyptian children after the Pharaoh would not free the Hebrews.  If Jaques is saying, like God, he would denounce first born sons, he is implying that he would include Duke Senior. 

The meaning of "ducdame" remains elusive. Scholars speculate that the origins of the word are Welsh, meaning "come hither." However, other scholars contend that it is a gypsy phrase which means, "I foretell." 

A pun on the legal term "names" as the "signature or borrowers."

Jacques is most likely referring to baboons, which look very dog-like.