By the word, "palms," Emerson is referring to the palm leaf or laurel branch, which in ancient times was used by people to celebrate a victory or occasion for rejoicing. One example of this usage well known to Emerson's contemporary readers was the palm-waving welcome that Jesus received when he entered Jerusalem on what is now celebrated as Palm Sunday.

This is a reference with religious overtones. A person who sets out to "gather immortal palms" is someone who aims at doing deeds or making discoveries that are worthy of great spiritual rejoicing. What Emerson is saying here is this: When you set out on such a quest, you shouldn't be constrained by prior rules or notions about what is supposed to be good. You have to be open to follow the dictates of your higher intuitions and conscience. These may go against conventional morals, or what authority figures tell you is right.

Emerson spells this out when we recounts memories from his youth. Emerson had expressed his lack of interest in keeping up religious traditions for tradition's sake. His friend had countered that Emerson shouldn't trust his inner dictates because they could be wrong.

"But these impulses may be from below, not from above."

Emerson says he replied,

"They do not seem to me to be such; but if I am the Devil's child, I will live then from the Devil."

Of course, Emerson doesn't believe his impulses come from the Devil, or that he follows the Devil. On the contrary, his argument is about rejecting blind obedience to rules. Trusting one's higher intuitions about what is right will lead to the discovery of true goodness.