According to Rabbi Moshe Greenwald (Arugat Habosem) in his Hallel Nirtzah Haggadah, these 15 steps also serve as a lesson plan for the leader of the Seder, who wishes to inspire others with words of Torah:
Before you can inspire others, you must sanctify yourself (Kadesh) and cleanse yourself (Urchatz) of sin.
In addition, you must break (Yachatz) your desires for pleasures (represented by the Karpas vegetable).
Only then can you tell others (Maggid) to cleanse themselves (Rachtzah).
When doing so, however, you must be careful to remove (Motzi) any strife (Matzah can also mean “strife”).
If you need to rebuke (Maror), sandwich (Korech) it within praise.
The teaching should then be as clear and straightforward as a “set table” (Shulchan Orech).
As an aspiring Torah teacher, accentuate the positive. Their inner (Tzafun) heart should be blessed (Beirach) by you, as you point out how they are truly good and holy.
If you rebuke in this manner, you will be praised (Hallel), and your actions will be pleasing (Nirtzah) before G‑d.
FIFTEEN WORDS
Some say that there are not necessarily 15 actions to take, but that each word of the rhyme is another step. Now, if you count them, you will find that there are 16!
The Rebbe explains7 that the final word, Nirztah, isn’t a step in our divine service. Instead, it is a promise from G‑d that He will accept our divine service, and ultimately we will merit the final Redemption.
1 See Haggadah Shleimah, preface ch. 16.
2 See Machzor Vitri, 65.
3 See Ohr Zerua 256. See also the Lubavitcher Rebbe in his Haggadah im Likutei Taamim Uminhagim, Simanei Seder.
4 See Haggadah im Likutei Taamim Uminhagim, Simanei Seder.
5 Alshich, Torat Moshe, Shemot 13:11-15.
6 Isaiah 58:7.
7 Haggadah im Likutei Taamim Uminhagim, Pirushim ubiurim, p. 80.