It is fairly well known that, in Israel, many recognize and observe seven days of pesach and a single seder whereas, outside of Israel, many recognize 8 days of pesach and two seders as proper observance.
Where did the extra day come from?
A piece over at my jewish learning does a good job explaining:

The Jewish calendar is lunar. Over 2,000 years ago, a council of rabbis from the Sanhedrin, the ancient legislative and judicial body, held special sessions in Jerusalem at the end of each lunar month to receive witnesses to the first sliver of the new moon. Because a lunar cycle is approximately 29 days long, it was no mystery when the new moon should appear, but the Sanhedrin still declared months and holidays only on the basis of these witnesses. …
Once the sighting was legitimated, the rabbis declared the next day Rosh Hodesh, the beginning of the new month. Originally, beacon fires would be set on mountaintops to spread the word to distant Jewish communities already living in far away places such as Egypt and Babylon. Watchers on faraway hills set their beacon fires as soon as they saw them, continuing the relay “until one could behold the whole of the Diaspora before him like a mass of fire” (Mishnah Rosh Hashanah 2:4)… Celebrating festivals for an extra day would ensure that, regardless of whatever confusion reigned about the exact start of the new month, at least one day of their celebration would be on the correct day.

Okay, that makes sense but we started to switch to a rule-based fixed-arithmetic lunisolar calendar system after the destruction of the second temple. That made the days designed to prevent error obsolete since everyone everywhere in the world used the same system and derived the days similarly. It no longer mattered how close one was to the Sanhedrin so why keep the extra days?
There are two major answers.
Our own BZ‘s:

At the end of Beitzah 4b that issue is addressed. “Now that we know the fixed new month, what’s the reason for doing two days?” The answer there is hizaharu b’minhag avoteichem (be careful about your ancestors’ minhag), because in the future there might be a decree preventing us from keeping the calendar…And we can even agree on the value of minhag avoteinu (see Beitzah 4b), and you can follow the minhag of your ancestors who kept 2 days, while I’ll follow the minhag of my ancestors who have been Reform for at least five generations.

The other common answer is given by a Rabbi from Aish here:

So why was a second day Yom Tov added? In order to make a distinction, to add to the Jewish awareness that one is living in the Diaspora and does not claim permanent residence in the Holy Land.

BZ’s answer to Minhag Avoteinu is compelling as is the issue that there has ceased to be a consistent mihag in the diaspora. The Reform, Renewal, Reconstructionist, and Conservative movements have all offered decisions permitting the use of a 7-day pesach. Here is some CCAR (Reform) analysis. The Cons and Recon movements both provide flexibility for local congregations but the result is that a majority of American Jews, and nearly all Israeli Jews fall under a 7-day authority. Many have been in such a situation for generations.
Now to respond to the idea that we should have an extra seder to remember we aren’t in Israel…
Was anyone really confused? In case you were here are ten ways to conclude you are in the US rather than in Israel that have nothing to do with extra days of passover.
10:The falafel is overpriced and underspiced.
9: Municipal services are transparent and efficient.
8: Sunday is for football not school.
7: Teacher strikes are generally limited to a few days, max.
6: People talk slowly and get uncomfortable with interruptions (supreme court excepted).
5: Holocaust jokes are rare and usually generate discomfort.
4: People have difficulty making political and religious assumptions based on the type of kippah a person is wearing. Many can’t remember the word and use “beanie” or “skull cap” instead.
3: Though people talk about God non-stop in government there aren’t religious parties associated with single religious approached.
2: Nation’s founders where individual rather than collective farmers.
1: Look around. No occupations and settlements for miles in any direction? You probably aren’t in Israel.*
*If you are, time for new bifocals.