The mnemonic/poem Kadesh, Urechatz etc. is attributed to the great commentator Rashi. According to several commentators it provides spiritual instructions as well.

Kadesh Urechatz: Sanctify (or separate) yourself from unhealthy behaviors and cleanse yourself from them.

Additionally, through the fulfillment of mitzvot, you sanctify yourself for the future and wash yourself of the spiritual maladies of the past. Torah is like an elixir that not only strengthens its patients for the future, it cures them of every previous illness and pain.

Karpas Yachatz: The humble vegetable teaches us to be modest and yielding by remembering that we are not perfect-our character is divided between good qualities and those that can improved.

Be satisfied with a simple vegetable dipped in salt water--karpas. But reserve this austerity for yourself. For the other, for the poor, fill their palm with plenty, and encourage them with soothing words. Perhaps you will say, "From where shall I have what to give to the poor?" The answer is: Yachatz-divide your bread, and give a portion to the less fortunate.

Sanctity and purify your behavior (kadesh-urechatz) and you will merit karpas-yachatz: The "harsh labor" of life (karpas), the yoke of financial worries, and other anxieties will be broken (yachatz) and removed from you.

Maggid Rachtzah: Don't be satisfied with your own spiritual work; reach out to others and teach them maggid. [Your efforts will be enhanced if you] consistently seek out and cleanse yourself (rachtzah) of character flaws.

Motzi means to extract (as in hamotzi lechem min ha'aretz: "Blessed are You, G‑d...who extracts bread from the earth").

Through your spiritual work, clarity, and reaching out to others, you will extract (motzi) your good inclination (matzah) from its dormancy and give it dominion over your life.

Maror Korech: Now that you have allowed your good inclination to emerge, wrap the matzah and maror together: Educate and elevate your evil inclination-symbolized by the maror--so that you may serve G‑d with both of your inclinations.

Additionally, in reaching out to others, incline your shoulder to help carry their burdens—wrap together (korech) their bitter woes (maror) and carry it for them.

Shulchan Orech: Remember that G‑d's table is always set; it is within His capacity to sustain those who trust in Him. By fulfilling all the above, you will merit a "set table" in this world and to the hidden blessings (tzafun-beirach) of the World to Come.

Tzafun Beirach: Recognize that there are two types of blessings in life: those we can clearly see and those we remain unaware of. Remember to thank G‑d not only for the revealed blessings and miracles but for the tzafun-beirach, the hidden blessings as well. Your praise of G‑d (hallel) is then complete and accepted (nirtzah).

Hallel Nirtzah: Some hidden blessings appear to us as troubles. Hallel means to praise G‑d for the good as well as what appears to us as negative. In the words of Rabbi Akiva: "All that the Merciful one does is for the good."

[Internalize the above, and you will] always be in a state of nirtzah, conditioned to accept favorably whatever challenges you may face. Anger and disappointment, even momentary, should become foreign and unknown.

From The Kehot Haggadah — // — authored and translated by Rabbi Yosef Marcus.