This is a day which many Chabad and other chassid groups hold dear because of the theme of second chances. I find this component very moving. Usually if you miss something you miss it, but here Hashem is saying, "I know it wasn't your fault that you missed out, please share your korban with Me." Pretty profound.
Sefer Hachinuch provides an even more powerful look at the mitzvah of Pesach Sheni. Pesach is one of the greatest examples of Hashem's awesome control over the world. Yitzeat mitzrayim, the amazing miracles, signs, and wonders He created to free us from bondage, produced a cornerstone of our belief in Him. Hashem wants everyone to have the opportunity to celebrate that belief and trust in His control over the world.
In spite of these two impressive reasons for Pesach Sheni, the lack of a Beit Hamikdash prevents much from happening today. There is a tradition to eat matza. People don't say Tachanun.
For a week my girls have been getting excited for Pesach Sheni (as a date between Yom Haatzmaut and Lag B'Omer). When I asked if they wanted matza pizza for lunch Gabi looked confused.
"But we don't eat matza pizza at seder," she replied.
"I don't like matza so much. Why can't we have charoset and marror?" Cohava added.
"Yes! Charoset! And huevos haminados!"
I didn't make it to the shops for marror, I wasn't cooking huevos haminados for 8 hours, and the charoset has to be nut-free, but I think they will still be happy at lunch time.