Reason In ancient Jerusalem, the Sanhedrin declared the new month based on testimony of at least two witnesses.  Since Jews who lived far from Jerusalem did not find out when the Jewish festivals began until as much as two weeks after the fact, a two-day festival was declared and we continue to observe that two-day holiday outside of Eretz Yisrael.
Situation You are in Eretz Yisrael for any of the Jewish festivals.  You want melacha done for you on the second day of the festival.
What To Do You may ask a resident of Eretz Yisrael to do melacha for you. (You may not ask a non-Jew to do melacha for you!)
Reason It is no longer a Jewish festival for him/her.
Note If you are outside of Eretz Yisrael, you may not ask a resident of Eretz Yisrael (who is visting you) to do melacha for you on the second day of the Jewish festival, even though he/she is no longer observing the festival.
Reason He/she may not do any melacha d'oraita even in private and not even for him/herself.